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## MCQ (More than One Correct Answer)

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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 $$\overrightarrow a = {{\widehat i -... IIT-JEE 2010 Paper 1 Offline ## MCQ (Single Correct Answer) More |$$\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 $$\left| {\matrix{ ... IIT-JEE 1989 Let$$OACB$$be a parallelogram with$$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$$re... IIT-JEE 1978 ## Fill in the Blanks More Let$$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

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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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