# 3D Geometry · Mathematics · JEE Advanced

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## MCQ (More than One Correct Answer)

JEE Advanced 2024 Paper 2 Online
A straight line drawn from the point $P(1,3,2)$, parallel to the line $\frac{x-2}{1}=\frac{y-4}{2}=\frac{z-6}{1}$, intersects the plane $L_1: x-y+3 z=... JEE Advanced 2024 Paper 1 Online Let$\mathbb{R}^3$denote the three-dimensional space. Take two points$P=(1,2,3)$and$Q=(4,2,7)$. Let$\operatorname{dist}(X, Y)denote the distanc... 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 z-20=0 \end{aligned} Whi... JEE Advanced 2022 Paper 1 Online Let $$S$$ be the reflection of a point $$Q$$ with respect to the plane given by $$\vec{r}=-(t+p) \hat{\imath}+t \hat{\jmath}+(1+p) \hat{k}$$ where... JEE Advanced 2020 Paper 2 Offline Let $$\alpha$$2 + $$\beta$$2 + $$\gamma$$2 $$\ne$$ 0 and $$\alpha$$ + $$\gamma$$ = 1. Suppose the point (3, 2, $$-$$1) is the mirror image of t... JEE Advanced 2020 Paper 1 Offline Let L1 and L2 be the following straight lines.$${L_1}:{{x - 1} \over 1} = {y \over { - 1}} = {{z - 1} \over 3}$$ and $${L_2}:{{x - 1} \over { - 3}} = ... JEE Advanced 2019 Paper 2 Offline Three lines$${L_1}:r = \lambda \widehat i$$,$$\lambda  \in $$R,$${L_2}:r = \widehat k + \mu \widehat j$$,$$\mu  \in $$R and$${L_3}:r =... JEE Advanced 2019 Paper 1 Offline Let L1 and L2 denote the lines$$r = \widehat i + \lambda ( - \widehat i + 2\widehat j + 2\widehat k)$$, $$\lambda$$$$\in$$ R and $$r = \mu (2\wide... JEE Advanced 2018 Paper 1 Offline Let P1 : 2x + y$$-$$z = 3 and P2 : x + 2y + z = 2 be two planes. Then, which of the following statement(s) is(are) TRUE? JEE Advanced 2016 Paper 1 Offline Consider a pyramid$$OPQRS$$located in the first octant$$\left( {x \ge 0,y \ge 0,z \ge 0} \right)$$with$$O$$as origin, and$$OP$$and$$OR$$alon... JEE Advanced 2015 Paper 1 Offline In$${R^3},$$consider the planes$$\,{P_1}:y = 0$$and$${P_2}:x + z = 1.$$Let$${P_3}$$be the plane, different from$${P_1}$$and$${P_2}$$, which... JEE Advanced 2015 Paper 1 Offline In$${R^3},$$let$$L$$be a straight lines passing through the origin. Suppose that all the points on$$L$$are at a constant distance from the two ... JEE Advanced 2014 Paper 1 Offline From a point$$P\left( {\lambda ,\lambda ,\lambda } \right),$$perpendicular$$PQ$$and$$PR$$are drawn respectively on the lines$$y=x, z=1$$and$$... JEE Advanced 2013 Paper 2 Offline Two lines $${L_1}:x = 5,{y \over {3 - \alpha }} = {z \over { - 2}}$$ and $${L_2}:x = \alpha ,{y \over { - 1}} = {z \over {2 - \alpha }}$$ are coplana... JEE Advanced 2013 Paper 1 Offline A line $$l$$ passing through the origin is perpendicular to the lines $$\,{l_1}:\left( {3 + t} \right)\widehat i + \left( { - 1 + 2t} \right)\wideha... IIT-JEE 2012 Paper 2 Offline If the straight lines$$\,{{x - 1} \over 2} = {{y + 1} \over k} = {z \over 2}$$and$${{x + 1} \over 5} = {{y + 1} \over 2} = {z \over k}$$are coplan... IIT-JEE 2006 Let$${\overrightarrow A }$$be vector parallel to line of intersection of planes$${P_1}$$and$${P_2}.$$Planes$${P_1}$$is parallel to the vector... ## MCQ (Single Correct Answer) JEE Advanced 2024 Paper 1 Online Let \gamma \in \mathbb{R} be such that the lines L_1: \frac{x+11}{1}=\frac{y+21}{2}=\frac{z+29}{3} and L_2: \frac{x+16}{3}=\frac{y+11}{2}=\frac{z... JEE Advanced 2023 Paper 1 Online Let \ell_1 and \ell_2 be the lines \vec{r}_1=\lambda(\hat{i}+\hat{j}+\hat{k}) and \vec{r}_2=(\hat{j}-\hat{k})+\mu(\hat{i}+\hat{k}), respective... JEE Advanced 2017 Paper 2 Offline The equation of the plane passing through the point (1, 1, 1) and perpendicular to the planes 2x + y$$-$$2z = 5 and 3x$$-$$6y$$-$$2z = 7 is JEE Advanced 2016 Paper 2 Offline Let$$P$$be the image of the point$$(3,1,7)$$with respect to the plane$$x-y+z=3.$$Then the equation of the plane passing through$$P$$and contai... JEE Advanced 2013 Paper 2 Offline Consider the lines$${L_1}:{{x - 1} \over 2} = {y \over { - 1}} = {{z + 3} \over 1},{L_2} : {{x - 4} \over 1} = {{y + 3} \over 1} = {{z + 3} \over 2}...
IIT-JEE 2012 Paper 2 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 distance $${2 \over {\sqrt 3 }}... IIT-JEE 2012 Paper 1 Offline The point$$P$$is the intersection of the straight line joining the points$$Q(2, 3, 5)$$and$$R(1, -1, 4)$$with the plane$$5x-4y-z=1.$$If$$S$$... IIT-JEE 2010 Paper 1 Offline Equation of the plane containing the straight line$${x \over 2} = {y \over 3} = {z \over 4}$$and perpendicular to the plane containing the straight ... IIT-JEE 2010 Paper 2 Offline If the distance of the point$$P(1, -2, 1)$$from the plane$$x+2y-2z\, = \alpha ,$$where$$\alpha > 0,$$is$$5,$$then the foot of the per... IIT-JEE 2010 Paper 2 Offline Match the statement in Column-$$I$$with the values in Column-$$II\,\,\,\,\,\,\,\,\,\,\,\,$$Column-$$I$$(A)$$\,\,\,\,$$A line fro... IIT-JEE 2009 Paper 2 Offline A line with positive direction cosines passes through the point P(2,$$-$$1, 2) and makes equal angles with the coordinate axes. The line meets the pl... IIT-JEE 2009 Paper 1 Offline Let$$P(3,2,6)$$be a point in space and$$Q$$be a point on the line$$$\widehat r = \left( {\widehat i - \widehat j + 2\widehat k} \right) + \mu \l... IIT-JEE 2008 Paper 2 Offline The distance of the point $$(1, 1, 1)$$ from the plane passing through the point $$(-1, -2, -1)$$ and whose normal is perpendicular to both the lines ... IIT-JEE 2008 Paper 1 Offline Consider three planes $${P_1}:x - y + z = 1$$$ $${P_2}:x + y - z = 1$$$$${P_3}:x - 3y + 3z = 2$$$ Let $${L_1},$$ $${L_2},$$ $${L_3}$$ be the line...
IIT-JEE 2007

## Subjective

IIT-JEE 2007
Consider the following linear equations $$ax+by+cz=0;$$ $$\,\,\,$$ $$bx+cy+az=0;$$ $$\,\,\,$$ $$cx+ay+bz=0$$ Match the conditions/expressions in Colu...
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 $${1 \over {\sqrt 6 }}$$ from the point $$(2, 1, -1).... IIT-JEE 2004 Find the equation of plane passing through$$(1, 1, 1)$$& parallel to the lines$${L_1},{L_2}$$having direction ratios$$(1,0,-1),(1,-1,0).$$Fi... IIT-JEE 2004 A parallelopiped$$'S'$$has base points$$A, B, C$$and$$D$$and upper face points$$A',B',C'$$and$$D'.$$This parallelopiped is compres... IIT-JEE 2004$${P_1}$$and$${P_2}$$are planes passing through origin.$${L_1}$$and$${L_2}$$are two line on$${P_1}$$and$${P_2}$$respectively such that thei... IIT-JEE 2003 (i) Find the equation of the plane passing through the points$$(2, 1, 0), (5, 0, 1)$$and$$(4, 1, 1).$$(ii) If$$P$$is the point$$(2, 1, 6)$$th... IIT-JEE 1996 The position vectors of the vertices$$A, B$$and$$C$$of a tetrahedron$$ABCD$$are$$\widehat i + \widehat j + \widehat k,\,\widehat i$$and$$3\wi...
IIT-JEE 1983
A vector $$\overrightarrow A$$ has components $${A_1},{A_2},{A_3}$$ in a right -handed rectangular Cartesian coordinate system $$oxyz.$$ The coordina...
IIT-JEE 1978
From a point $$O$$ inside a triangle $$ABC,$$ perpendiculars $$OD$$, $$OE, OF$$ are drawn to the sides $$BC, CA, AB$$ respectively. Prove that the pe...

## Fill in the Blanks

IIT-JEE 1994
A unit vector perpendicular to the plane determined by the points $$P\left( {1, - 1,2} \right)Q\left( {2,0, - 1} \right)$$ and $$R\left( {0,2,1} \righ... IIT-JEE 1983 The unit vector perpendicular to the plane determined by$$P\left( {1, - 1,2} \right),\,Q\left( {2,0, - 1} \right)$$and$$R\left( {0,2,1} \right)$$i... IIT-JEE 1983 The area of the triangle whose vertices are$$A(1, -1, 2), B(2, 1, -1), C(3, -1, 2) is ..........
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