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## MCQ (More than One Correct Answer)

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Let $\hat{\imath}, \hat{\jmath}$ and $\hat{k}$ be the unit vectors along the three positive coordinate axes. Let $$\be... JEE Advanced 2022 Paper 2 Online Let$$S$$be the reflection of a point$$Q$$with respect to the plane given by$$ \vec{r}=-(t+p) \hat{\imath}+t \hat{\...
JEE Advanced 2022 Paper 1 Online
Let $$P_{1}$$ and $$P_{2}$$ be two planes given by \begin{aligned} &P_{1}: 10 x+15 y+12 z-60=0 \\ &P_{2}:-2 x+5 y+4 ... JEE Advanced 2022 Paper 1 Online Let O be the origin and\overrightarrow {OA} = 2\widehat i + 2\widehat j + \widehat k$$and$$\overrightarrow {OB} =...
JEE Advanced 2021 Paper 2 Online
Let a and b be positive real numbers. Suppose $$PQ = a\widehat i + b\widehat j$$ and $$PS = a\widehat i - b\widehat j$$ ...
JEE Advanced 2020 Paper 2 Offline
Let $$\alpha$$2 + $$\beta$$2 + $$\gamma$$2 $$\ne$$ 0 and $$\alpha$$ + $$\gamma$$ = 1. Suppose the point (3, 2, $$... JEE Advanced 2020 Paper 2 Offline Let L1 and L2 be the following straight lines.$${L_1}:{{x - 1} \over 1} = {y \over { - 1}} = {{z - 1} \over 3}$$and$${...
JEE Advanced 2020 Paper 1 Offline
Three lines $${L_1}:r = \lambda \widehat i$$, $$\lambda$$ $$\in$$ R,$${L_2}:r = \widehat k + \mu \widehat j$$, $$\mu ... JEE Advanced 2019 Paper 2 Offline Let L1 and L2 denote the lines$$r = \widehat i + \lambda ( - \widehat i + 2\widehat j + 2\widehat k)$$,$$\lambda  \...
JEE Advanced 2019 Paper 1 Offline
Let P1 : 2x + y $$-$$ z = 3 and P2 : x + 2y + z = 2 be two planes. Then, which of the following statement(s) is(are) TR...
JEE Advanced 2018 Paper 1 Offline
Let $$\widehat u = {u_1} \widehat i + {u_2}\widehat j + {u_3}\widehat k$$ be a unit vector in $${{R^3}}$$ and $$\widehat... JEE Advanced 2016 Paper 2 Offline Consider a pyramid$$OPQRS$$located in the first octant$$\left( {x \ge 0,y \ge 0,z \ge 0} \right)$$with$$O$$as orig... JEE Advanced 2016 Paper 1 Offline Let$$\Delta PQR$$be a triangle. Let$$\vec a = \overrightarrow {QR} ,\vec b = \overrightarrow {RP} $$and$$\overright...
JEE Advanced 2015 Paper 1 Offline
In $${R^3},$$ let $$L$$ be a straight lines passing through the origin. Suppose that all the points on $$L$$ are at a c...
JEE Advanced 2015 Paper 1 Offline
In $${R^3},$$ consider the planes $$\,{P_1}:y = 0$$ and $${P_2}:x + z = 1.$$ Let $${P_3}$$ be the plane, different from ...
JEE Advanced 2015 Paper 1 Offline
Let $$\overrightarrow x ,\overrightarrow y$$ and $$\overrightarrow z$$ be three vectors each of magnitude $$\sqrt 2$$...
JEE Advanced 2014 Paper 1 Offline
Two lines $${L_1}:x = 5,{y \over {3 - \alpha }} = {z \over { - 2}}$$ and $${L_2}:x = \alpha ,{y \over { - 1}} = {z \over... JEE Advanced 2013 Paper 2 Offline A line$$l$$passing through the origin is perpendicular to the lines$$$\,{l_1}:\left( {3 + t} \right)\widehat i + \le... JEE Advanced 2013 Paper 1 Offline If the straight lines $$\,{{x - 1} \over 2} = {{y + 1} \over k} = {z \over 2}$$ and $${{x + 1} \over 5} = {{y + 1} \over... IIT-JEE 2012 Paper 2 Offline The vector (s) which is/are coplanar with vectors$${\widehat i + \widehat j + 2\widehat k}$$and$${\widehat i + 2\wide... IIT-JEE 2011 Paper 1 Offline Let $${\overrightarrow A }$$ be vector parallel to line of intersection of planes $${P_1}$$ and $${P_2}.$$ Planes $${P_... IIT-JEE 2006 Let$$a$$and$$b$$two non-collinear unit vectors. If$$u = a - \left( {a\,.\,b} \right)\,b$$and$$v = a \times b,$$t... IIT-JEE 1999 Which of the following expressions are meaningful? IIT-JEE 1998 The vector$$\,{1 \over 3}\left( {2\widehat i - 2\widehat j + \widehat k} \right)$$is IIT-JEE 1994 Let$$\vec a = 2\hat i - \hat j + \hat k,\vec b = \hat i + 2\hat j - \hat k$$and$$\overrightarrow c = \widehat i + \... IIT-JEE 1993 ## Numerical More Let $$\overrightarrow u$$, $$\overrightarrow v$$ and $$\overrightarrow w$$ be vectors in three-dimensional space, whe... JEE Advanced 2021 Paper 1 Online Let $$\alpha$$, $$\beta$$ and $$\gamma$$ be real numbers such that the system of linear equationsx + 2y + 3z = $$\alpha... JEE Advanced 2021 Paper 1 Online Let$$\alpha$$,$$\beta$$and$$\gamma$$be real numbers such that the system of linear equationsx + 2y + 3z =$$\alpha$...
JEE Advanced 2021 Paper 1 Online
Let $$\overrightarrow a = 2\widehat i + \widehat j - \widehat k$$ and $$\overrightarrow b = \widehat i + 2\widehat j + \... JEE Advanced 2019 Paper 2 Offline Three lines are given by$$r = \lambda \widehat i,\,\lambda \in R$$,$$r = \mu (\widehat i + \widehat j),\,\mu \in R$$... JEE Advanced 2019 Paper 1 Offline Let P be a point in the first octant, whose image Q in the plane x + y = 3 (that is, the line segment PQ is perpendicula... JEE Advanced 2018 Paper 2 Offline Let a and b be two unit vectors such that a . b = 0. For some x, y$$ \in $$R, let$$\overrightarrow c = x\overrightarro...
JEE Advanced 2018 Paper 1 Offline
Suppose that $$\overrightarrow p ,\overrightarrow q$$ and $$\overrightarrow r$$ are three non-coplanar vectors in $${R... JEE Advanced 2015 Paper 2 Offline Let$$\overrightarrow a \,\,,\,\,\overrightarrow b $$and$$\overrightarrow c $$be three non-coplanar unit vectors such... JEE Advanced 2014 Paper 1 Offline Consider the set of eight vectors$$V = \left\{ {a\widehat i + b\widehat j + c\widehat k:a,b.c \in \left\{ { - 1,1} \ri...
JEE Advanced 2013 Paper 1 Offline
If $$\overrightarrow a ,\overrightarrow b$$ and $$\overrightarrow c$$ are unit vectors satisfying $${\left| {\overrig... IIT-JEE 2012 Paper 1 Offline Let$$\overrightarrow a = - \widehat i - \widehat k,\overrightarrow b = - \widehat i + \widehat j$$and$$\overright...
IIT-JEE 2011 Paper 2 Offline
If the distance between the plane $$Ax-2y+z=d$$ and the plane containing the lines $${{x - 1} \over 2} = {{y - 2} \over ... IIT-JEE 2010 Paper 1 Offline If$$\overrightarrow a $$and$$\overrightarrow b $$are vectors in space given by$$\overrightarrow a = {{\widehat i -...
IIT-JEE 2010 Paper 1 Offline

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|$$\overrightarrow{OX}$$ $$\times$$ $$\overrightarrow{OY}$$| = ?
JEE Advanced 2017 Paper 2 Offline
If the triangle PQR varies, then the minimum value of cos(P + Q) + cos(Q + R) + cos(R + P) is
JEE Advanced 2017 Paper 2 Offline
The equation of the plane passing through the point (1, 1, 1) and perpendicular to the planes 2x + y $$-$$ 2z = 5 and 3x...
JEE Advanced 2017 Paper 2 Offline
Let O be the origin and let PQR be an arbitrary triangle. The point S is such that$$\overrightarrow{OP}$$ . $$\overright... JEE Advanced 2017 Paper 2 Offline Let$$P$$be the image of the point$$(3,1,7)$$with respect to the plane$$x-y+z=3.$$Then the equation of the plane pa... JEE Advanced 2016 Paper 2 Offline Match the following :$$\,\,\,\,\,\,\,\,\,\,\,\,$$Column$$I$$(A)$$\,\,\,\,$$In a triangle$$\Delta XYZ,$... JEE Advanced 2015 Paper 1 Offline Match the following : $$\,\,\,\,$$ $$\,\,\,\,$$ $$\,\,\,\,$$ Column $$I$$ (A)$$\,\,\,\,$$ In $${R^2},$$ If the magnitu... JEE Advanced 2015 Paper 1 Offline From a point $$P\left( {\lambda ,\lambda ,\lambda } \right),$$ perpendicular $$PQ$$ and $$PR$$ are drawn respectively on... JEE Advanced 2014 Paper 1 Offline Consider the lines $${L_1}:{{x - 1} \over 2} = {y \over { - 1}} = {{z + 3} \over 1},{L_2} : {{x - 4} \over 1} = {{y + 3}... JEE Advanced 2013 Paper 2 Offline match List$$I$$with List$$II$$and select the correct answer using the code given below the lists:$$\,\,\,\,\... JEE Advanced 2013 Paper 2 Offline The point $$P$$ is the intersection of the straight line joining the points $$Q(2, 3, 5)$$ and $$R(1, -1, 4)$$ with the ... IIT-JEE 2012 Paper 1 Offline The equation of a plane passing through the line of intersection of the planes $$x+2y+3z=2$$ and $$x-y+z=3$$ and at a di... IIT-JEE 2012 Paper 2 Offline If $$\overrightarrow a$$ and $$\overrightarrow b$$ are vectors such that $$\left| {\overrightarrow a + \overrightarr... IIT-JEE 2012 Paper 2 Offline Match the statements given in Column -$$I$$with the values given in Column-$$II.\,\,\,\,\,\,\,\,\,\,\,\,... IIT-JEE 2011 Paper 2 Offline Let $$\overrightarrow a = \widehat i + \widehat j + \widehat k,\,\overrightarrow b = \widehat i - \widehat j + \wideha... IIT-JEE 2011 Paper 1 Offline Match the statement in Column-$$I$$with the values in Column-$$II\,\,\,\,\,\,\,\,\,\,\,\,$$Column-$$I... IIT-JEE 2010 Paper 2 Offline Equation of the plane containing the straight line $${x \over 2} = {y \over 3} = {z \over 4}$$ and perpendicular to the ... IIT-JEE 2010 Paper 1 Offline If the distance of the point $$P(1, -2, 1)$$ from the plane $$x+2y-2z$$$$\, = \alpha ,$$ where $$\alpha &gt; 0,$$ is$...
IIT-JEE 2010 Paper 2 Offline
Two adjacent sides of a parallelogram $$ABCD$$ are given by $$\overrightarrow {AB} = 2\widehat i + 10\widehat j + 11\w... IIT-JEE 2010 Paper 2 Offline Let$$P,Q,R$$and$$S$$be the points on the plane with position vectors$${ - 2\widehat i - \widehat j,4\widehat i,3\wi...
IIT-JEE 2010 Paper 1 Offline
A line with positive direction cosines passes through the point $$P(2, -1, 2)$$ and makes equal angles with the coordina...
IIT-JEE 2009
Let $$P(3,2,6)$$ be a point in space and $$Q$$ be a point on the line $$\widehat r = \left( {\widehat i - \widehat j +... IIT-JEE 2009 If$$\overrightarrow a \,,\,\overrightarrow b ,\overrightarrow c $$and$$\overrightarrow d $$are unit vectors such tha... IIT-JEE 2009 Consider three planes$$${P_1}:x - y + z = 1${P_2}:x + y - z = 1${P_3}:x - 3y + 3z = 2$$Let$${L_1},... IIT-JEE 2008 Consider the lines $${L_1}:{{x + 1} \over 3} = {{y + 2} \over 1} = {{z + 1} \over 2}\,\,\,\,{L_2}:{{x - 2} \over 1} = ... IIT-JEE 2008 Consider the lines$${L_1}:{{x + 1} \over 3} = {{y + 2} \over 1} = {{z + 1} \over 2}\,\,\,\,{L_2}:{{x - 2} \over 1} = {... IIT-JEE 2008 Consider the lines $${L_1}:{{x + 1} \over 3} = {{y + 2} \over 1} = {{z + 1} \over 2}\,\,\,\,{L_2}:{{x - 2} \over 1} = {... IIT-JEE 2008 The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors$$\overrightarrow a \,,\,... IIT-JEE 2008 Let two non-collinear unit vectors $$\widehat a$$ and $$\widehat b$$ form an acute angle. A point $$P$$ moves so that at... IIT-JEE 2008 Let the vectors $$\overrightarrow {PQ} ,\,\,\overrightarrow {QR} ,\,\,\overrightarrow {RS} ,\,\,\overrightarrow {ST} ,\,... IIT-JEE 2007 Consider the planes$$3x-6y-2z=15$$and$$2x+y-2z=5.$$STATEMENT-1: The parametric equations of the line of intersectio... IIT-JEE 2007 Let$$\overrightarrow a \,,\,\overrightarrow b ,\overrightarrow c $$be unit vectors such that$${\overrightarrow a + ... IIT-JEE 2007 The minimum of distinct real values of $$\lambda ,$$ for which the vectors $$- {\lambda ^2}\widehat i + \widehat j + \w... IIT-JEE 2007 Let$$\overrightarrow a = \widehat i + 2\widehat j + \widehat k,\,\overrightarrow b = \widehat i - \widehat j + \wideh... IIT-JEE 2006 A plane which is perpendicular to two planes $$2x - 2y + z = 0$$ and $$x - y + 2z = 4,$$ passes through $$(1, -2, 1).$$ ... IIT-JEE 2006 If $$\overrightarrow a \,,\,\overrightarrow b ,\overrightarrow c$$ are three non-zero, non-coplanar vectors and $$\ov... IIT-JEE 2005 Screening A variable plane at a distance of the one unit from the origin cuts the coordinates axes at$$A,B$$and$$C.$$If t... IIT-JEE 2005 Screening The unit vector which is orthogonal to the vector$$3\overrightarrow i + 2\overrightarrow j + 6\overrightarrow k $$an... IIT-JEE 2004 Screening If the lines$${{x - 1} \over 2} = {{y + 1} \over 3} = {{z - 1} \over 4}$$and$$\,{{x - 3} \over 1} = {{y - k} \over 2}... IIT-JEE 2004 Screening If $$\overrightarrow a = \left( {\widehat i + \widehat j + \widehat k} \right),\overrightarrow a .\overrightarrow b = ... IIT-JEE 2004 Screening The value of$$'a'$$so that the volume of parallelopiped formed by$$\widehat i + a\widehat j + \widehat k,\widehat j +... IIT-JEE 2003 Screening The value of $$k$$ such that $${{x - 4} \over 1} = {{y - 2} \over 1} = {{z - k} \over 2}$$ lies in the plane $$2x -4y +z... IIT-JEE 2003 Screening Let$$\overrightarrow V = 2\overrightarrow i + \overrightarrow j - \overrightarrow k $$and$$\overrightarrow W = \o... IIT-JEE 2002 Screening If $${\overrightarrow a }$$ and $${\overrightarrow b }$$ are two unit vectors such that $${\overrightarrow a + 2\overri... IIT-JEE 2002 Screening If$$\overrightarrow a \,,\,\overrightarrow b $$and$$\overrightarrow c $$are unit vectors, then$${\left| {\overright... IIT-JEE 2001 Screening Let $$\overrightarrow a = \overrightarrow i - \overrightarrow k ,\overrightarrow b = x\overrightarrow i + \overright... IIT-JEE 2001 Screening If$$\overrightarrow a \,,\,\overrightarrow b $$and$$\overrightarrow c $$are unit coplanar vectors, then the scalar t... IIT-JEE 2000 Screening Let the vectors$$\overrightarrow a ,\overrightarrow b ,\overrightarrow c $$and$$\overrightarrow d $$be such that$$... IIT-JEE 2000 Screening If the vectors $$\overrightarrow a ,\overrightarrow b$$ and $$\overrightarrow c$$ form the sides $$BC,$$ $$CA$$ and $$... IIT-JEE 2000 Screening Let$$a=2i+j+k, b=i+2j-k$$and a unit vector$$c$$be coplanar. If$$c$$is perpendicular to$$a,$$then$$c =$$IIT-JEE 1999 Let$$a=2i+j-2k$$and$$b=i+j.$$If$$c$$is a vector such that$$a.c = \left| c \right|,\left| {c - a} \right| = ... IIT-JEE 1999 For three vectors $$u,v,w$$ which of the following expression is not equal to any of the remaining three? IIT-JEE 1998 If $$a = i + j + k,\overrightarrow b = 4i + 3j + 4k$$ and $$c = i + \alpha j + \beta k$$ are linearly dependent vector... IIT-JEE 1998 If $$\overrightarrow a ,$$ $$\overrightarrow b$$ and $$\overrightarrow c$$ are three non coplanar vectors, then $$\l... IIT-JEE 1995 Screening Let$$\overrightarrow u ,\overrightarrow v $$and$$\overrightarrow w $$be vectors such that$$\overrightarrow u + \ov... IIT-JEE 1995 Screening If $$\overrightarrow a ,\overrightarrow b ,\overrightarrow c$$ are non coplanar unit vectors such that $$\overrightarro... IIT-JEE 1995 Screening Let$$\overrightarrow a = \widehat i - \widehat j,\overrightarrow b = \widehat j - \widehat k,\overrightarrow c = \wi... IIT-JEE 1995 Screening Let $$\alpha ,\beta ,\gamma$$ be distinct real numbers. The points with position vectors $$\alpha \widehat i + \beta \... IIT-JEE 1994 Let$$\overrightarrow p $$and$$\overrightarrow q $$be the position vectors of$$P$$and$$Q$$respectively, with resp... IIT-JEE 1994 Let$$a, b, c$$be distinct non-negative numbers. If the vectors$$a\widehat i + a\widehat j + c\widehat k,\widehat i + ... IIT-JEE 1993 Let $$\overrightarrow a ,\overrightarrow b ,\overrightarrow c ,$$ be three non-coplanar vectors and $$\overrightarrow p ... IIT-JEE 1988 The number of vectors of unit length perpendicular to vectors$$\overrightarrow a = \left( {1,1,0} \right)$$and$$\ove... IIT-JEE 1987 Let $$\overrightarrow a = {a_1}i + {a_2}j + {a_3}k,\,\,\,\overrightarrow b = {b_1}i + {b_2}j + {b_3}k$$ and $$\overrig... IIT-JEE 1986 The volume of the parallelopiped whose sides are given by$$\overrightarrow {OA} = 2i - 2j,\,\overrightarrow {OB} = i... IIT-JEE 1983 The points with position vectors $$60i+3j,$$ $$40i-8j,$$ $$ai-52j$$ are collinear if IIT-JEE 1983 For non-zero vectors $${\overrightarrow a ,\,\overrightarrow b ,\overrightarrow c },$$ $$\left| {\left( {\overrightarrow... IIT-JEE 1982 The scalar$$\overrightarrow A .\left( {\overrightarrow B + \overrightarrow C } \right) \times \left( {\overrightarrow ... IIT-JEE 1981 ## Subjective More Match the statements/expressions given in Column-$$I$$ with the values given in Column-$$II.$$ $$\,\,\,\,\,$$ $$\,\,\,\,... IIT-JEE 2009 Match the statements / expressions given in Column-$$I$$with the values given in Column-$$II.\,\,\,\,\,\,\,\... IIT-JEE 2009 Consider the following linear equations $$ax+by+cz=0;$$ $$\,\,\,$$ $$bx+cy+az=0;$$ $$\,\,\,$$ $$cx+ay+bz=0$$ Match the ... IIT-JEE 2007 Match the folowing : (A)$$\,\,\,$$Two rays $$x + y = \left| a \right|$$ and $$ax - y=1$$ intersects each other in the$...
IIT-JEE 2006
If the incident ray on a surface is along the unit vector $$\widehat v\,\,,$$ the reflected ray is along the unit vector...
IIT-JEE 2005
Find the equation of the plane containing the line $$2x-y+z-3=0,3x+y+z=5$$ and at a distance of $${1 \over {\sqrt 6 }}$$...
IIT-JEE 2005
$${P_1}$$ and $${P_2}$$ are planes passing through origin. $${L_1}$$ and $${L_2}$$ are two line on $${P_1}$$ and $${P_2}... IIT-JEE 2004 If$$\overrightarrow a ,\overrightarrow b ,\overrightarrow c $$and$$\overrightarrow d $$are distinct vectors such tha... IIT-JEE 2004 Find the equation of plane passing through$$(1, 1, 1)$$&amp; parallel to the lines$${L_1},{L_2}$$having direction ra... IIT-JEE 2004 A parallelopiped$$'S'$$has base points$$A, B, C$$and$$D$$and upper face points$$A',B',C'$$and$$D'.$$... IIT-JEE 2004 (i) Find the equation of the plane passing through the points$$(2, 1, 0), (5, 0, 1)$$and$$(4, 1, 1).$$(ii) If$$P$$... IIT-JEE 2003 If$$\overrightarrow u ,\overrightarrow v ,\overrightarrow w ,$$are three non-coplanar unit vectors and$$\alpha ,\beta...
IIT-JEE 2003
Let $$V$$ be the volume of the parallelopiped formed by the vectors $$\overrightarrow a = {a_1}\widehat i + {a_2}\wideh... IIT-JEE 2002 Let$$\overrightarrow A \left( t \right) = {f_1}\left( t \right)\widehat i + {f_2}\left( t \right)\widehat j$$and$$$\... IIT-JEE 2001 Find $$3-$$dimensional vectors $${\overrightarrow v _1},{\overrightarrow v _2},{\overrightarrow v _3}$$ satisfying $$\... IIT-JEE 2001 Show, by vector methods, that the angular bisectors of a triangle are concurrent and find an expression for the position... IIT-JEE 2001 Let$$u$$and$$v$$be units vectors. If$$w$$is a vector such that$$w + \left( {w \times u} \right) = v,$$then prove... IIT-JEE 1999 For any two vectors$$u$$and$$v,$$prove that (a)$${\left( {u\,.\,v} \right)^2} + {\left| {u \times v} \right|^2} = ... IIT-JEE 1998 Prove, by vector methods or otherwise, that the point of intersection of the diagonals of a trapezium lies on the line p... IIT-JEE 1998 If $$A,B$$ and $$C$$ are vectors such that $$\left| B \right| = \left| C \right|.$$ Prove that $$\left[ {\left( {A + B}... IIT-JEE 1997 The position vectors of the vertices$$A, B$$and$$C$$of a tetrahedron$$ABCD$$are$$\widehat i + \widehat j + \wideh... IIT-JEE 1996 If the vectors $$\overrightarrow b ,\overrightarrow c ,\overrightarrow d ,$$ are not coplanar, then prove that the vecto... IIT-JEE 1994 In a triangle $$ABC, D$$ and $$E$$ are points on $$BC$$ and $$AC$$ respectively, such that $$BD=2DC$$ and $$AE=3EC.$$ Le... IIT-JEE 1993 Determine the value of $$'c'$$ so that for all real $$x,$$ the vector $$cx\widehat i - 6\widehat j - 3\widehat k$$ and ... IIT-JEE 1991 Let $$\overrightarrow A = 2\overrightarrow i + \overrightarrow k ,\,\overrightarrow B = \overrightarrow i + \overrig... IIT-JEE 1990 In a triangle$$OAB,E$$is the midpoint of$$BO$$and$$D$$is a point on$$AB$$such that$$AD:DB=2:1.$$If$$OD$$and ... IIT-JEE 1989 If vectors$$\overrightarrow A ,\overrightarrow B ,\overrightarrow C $$are coplanar, show that$$$\left| {\matrix{ ...
IIT-JEE 1989
Let $$OA$$ $$CB$$ be a parallelogram with $$O$$ at the origin and $$OC$$ a diagonal. Let $$D$$ be the midpoint of $$OA.... IIT-JEE 1988 If$$A, B, C, D$$are any four points in space, prove that -$$\left| {\overrightarrow {AB} \times \overrightarrow {CD...
IIT-JEE 1987
The position vectors of the points $$A, B, C$$ and $$D$$ are $$3\widehat i - 2\widehat j - \widehat k,\,2\widehat i + 3\... IIT-JEE 1986 A vector$$\overrightarrow A $$has components$${A_1},{A_2},{A_3}$$in a right -handed rectangular Cartesian coordinate... IIT-JEE 1983 Find all values of$$\lambda $$such that$$x, y, z,\, \ne (0,0,0)$$and$$\left( {\overrightarrow i + \overri...
IIT-JEE 1982
$${A_1},{A_2},.................{A_n}$$ are the vertices of a regular plane polygon with $$n$$ sides and $$O$$ is its cen...
IIT-JEE 1982
From a point $$O$$ inside a triangle $$ABC,$$ perpendiculars $$OD$$, $$OE, OF$$ are drawn to the sides $$BC, CA, AB$$ re...
IIT-JEE 1978

## Fill in the Blanks

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Let $$OA=a,$$ $$OB=10a+2b$$ and $$OC=b$$ where $$O,A$$ and $$C$$ are non-collinear points. Let $$p$$ denote the area of ...
IIT-JEE 1997
A nonzero vector $$\overrightarrow a$$ is parallel to the line of intersection of the plane determined by the vectors $... IIT-JEE 1996 If $$\overrightarrow b \,$$ and $$\overrightarrow c \,$$ are two non-collinear unit vectors and $$\overrightarrow a \,$$... IIT-JEE 1996 A unit vector perpendicular to the plane determined by the points $$P\left( {1, - 1,2} \right)Q\left( {2,0, - 1} \right)... IIT-JEE 1994 A unit vector coplanar with$$\overrightarrow i + \overrightarrow j + 2\overrightarrow k $$and$$\overrightarrow i +... IIT-JEE 1992 Given that $$\overrightarrow a = \left( {1,1,1} \right),\,\,\overrightarrow c = \left( {0,1, - 1} \right),\,\overright... IIT-JEE 1991 The components of a vector$$\overrightarrow a $$along and perpendicular to a non-zero vector$$\overrightarrow b $$ar... IIT-JEE 1988 Let$$b = 4\widehat i + 3\widehat j$$and$$\overrightarrow c $$be two vectors perpendicular to each other in the$$xy$...
IIT-JEE 1987
If the vectors $$a\widehat i + \widehat j + \widehat k,\,\,\widehat i + b\widehat j + \widehat k$$ and $$\widehat i + \... IIT-JEE 1987 If$$\overrightarrow A = \left( {1,1,1} \right),\,\,\overrightarrow C = \left( {0,1, - 1} \right)$$are given vectors,... IIT-JEE 1985 If$$\overrightarrow A \overrightarrow {\,B} \overrightarrow {\,C} $$are three non-coplannar vectors, then -$${{\over...
IIT-JEE 1985
If $$\left| {\matrix{ a &amp; {{a^2}} &amp; {1 + {a^3}} \cr b &amp; {{b^2}} &amp; {1 + {b^3}} \cr c &amp; {... IIT-JEE 1985$$A, B, C$$and$$D,$$are four points in a plane with position vectors$$a, b, c$$and$$d$$respectively such that$$$... IIT-JEE 1984 The area of the triangle whose vertices are $$A(1, -1, 2), B(2, 1, -1), C(3, -1, 2)$$ is .......... IIT-JEE 1983 The unit vector perpendicular to the plane determined by $$P\left( {1, - 1,2} \right),\,Q\left( {2,0, - 1} \right)$$ and... IIT-JEE 1983 Let $$\overrightarrow A ,\overrightarrow B ,\overrightarrow C$$ be vectors of length $$3, 4, 5$$ respectively. Let $$\o... IIT-JEE 1981 ## True or False More For any three vectors$${\overrightarrow a ,\,\overrightarrow b ,}$$and$${\overrightarrow c ,}\left( {\overright... IIT-JEE 1989 The points with position vectors $$a+b,$$ $$a-b,$$ and $$a+kb$$ are collinear for all real values of $$k.$$ IIT-JEE 1984 If $$X.A=0, X.B=0, X.C=0$$ for some non-zero vector $$X,$$ then $$\left[ {A\,B\,C} \right] = 0$$ IIT-JEE 1983 Let $$\overrightarrow A ,\overrightarrow B$$ and $${\overrightarrow C }$$ be unit vectors suppose that$\$\overrightarro...
IIT-JEE 1981

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