New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

3D Geometry question

2015 · Shift 1 · Q34

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Advanced
Mathematics
3D Geometry
2015 · Shift 1 · Q34

3D Geometry question

2015 · Shift 1 · Q34

JEE AdvancedMathematics3D GeometryMultiple correct+4 / −1

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 planes

{P_1}:x + 2y - z + 1 = 0

and

{P_2}:2x - y + z - 1 = 0.

Let

M

be the locus of the feet of the perpendiculars drawn from the points on

L

to the plane

{P_1}.

Which of the following points lie (s) on

M

?

A
$\left( {0, - {5 \over 6}, - {2 \over 3}} \right)$
B
$\left( { - {1 \over 6}, - {1 \over 3},{1 \over 6}} \right)$
C
$\left( { - {5 \over 6},0,{1 \over 6}} \right)$
D
$\left( { - {1 \over 3},0,{2 \over 3}} \right)$

More from 3D Geometry

From a point $P (λ, λ, λ),$ perpendicular $P Q$ and $P R$ are drawn respectively on the lines $y = x, z = 1$ and $y = - x, z = - 1.$ If $P$ is such that $∠ QP R$ is a right angle, then the possible value(s) of $λ$ …2014 · Multiple correct
Perpendiculars are drawn from points on the line $\frac{x + 2}{2} = \frac{y + 1}{- 1} = \frac{z}{3}$ to the plane $x + y + z = 3$ . The foot of perpendiculars lie on the line2013 · MCQ
A line $l$ passing through the origin is perpendicular to the lines $l_{1} : (3 + t) i + (- 1 + 2 t) j + (4 + 2 t) k, - \infty < t < \infty l_{2} : (3 + 2 s) i + (3 + 2 s) j + (2 + s) k, - \infty < s < \infty$ …2013 · Multiple correct
Consider the lines $L_{1} : \frac{x - 1}{2} = \frac{y}{- 1} = \frac{z + 3}{1}, L_{2} : \frac{x - 4}{1} = \frac{y + 3}{1} = \frac{z + 3}{2}$ and the planes $P_{1} : 7 x + y + 2 z = 3, P_{2} = 3 x + 5 y - 6 z = 4.$ Let $a x + b y + cz = d$ be…2013 · MCQ
Two lines $L_{1} : x = 5, \frac{y}{3 - α} = \frac{z}{- 2}$ and $L_{2} : x = α, \frac{y}{- 1} = \frac{z}{2 - α}$ are coplanar. Then $α$ can take value(s)2013 · Multiple correct
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 $5 x - 4 y - z = 1.$ If $S$ is the foot of the perpendicular drawn from the point $T (2, 1, 4)$ to $QR,$ then the length of the…2012 · MCQ
If the straight lines $\frac{x - 1}{2} = \frac{y + 1}{k} = \frac{z}{2}$ and $\frac{x + 1}{5} = \frac{y + 1}{2} = \frac{z}{k}$ are coplanar, then the plane (s) containing these two lines is (are)2012 · Multiple correct
The equation of a plane passing through the line of intersection of the planes $x + 2 y + 3 z = 2$ and $x - y + z = 3$ and at a distance $\frac{2}{3}$ from the point $(3, 1, - 1)$ is2012 · MCQ