EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 16th April 2018>Q 103

MEDIUM

JEE Main

IMPORTANT

Earn 100

The sum of the intercepts on the coordinate axes of the plane passing through the point $(- 2, - 2, 2)$ and containing the line joining the points $(1, - 1, 2)$ and $(1, 1, 1)$ is

50% studentsanswered this correctly

Important Questions on Three Dimensional Geometry

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 16th April 2018>Q 104

If the angle between the lines

\frac{x}{2} = \frac{y}{2} = \frac{z}{1}

and

\frac{5 - x}{- 2} = \frac{7 y - 14}{P} = \frac{z - 3}{4}

is

\cos^{- 1} (\frac{2}{3}),

then

P

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 2nd April 2017>Q 105

If the image of the point

P (1, - 2, 3)

in the plane,

2 x + 3 y - 4 z + 22 = 0

measured parallel to the line,

\frac{x}{1} = \frac{y}{4} = \frac{z}{5}

is

Q

, then

P Q

is equal to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 2nd April 2017>Q 106

The distance of the point

(1, 3, - 7)

from the plane passing through the point

(1, - 1, - 1)

, having normal perpendicular to both the lines

\frac{x - 1}{1} = \frac{y + 2}{- 2} = \frac{z - 4}{3}

and

\frac{x - 2}{2} = \frac{y + 1}{- 1} = \frac{z + 7}{- 1}

, is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 8th April 2017>Q 107

The coordinates of the foot of the perpendicular from the point

(1, - 2, 1)

on the plane containing the lines

\frac{x + 1}{6} = \frac{y - 1}{7} = \frac{z - 3}{8}

and

\frac{x - 1}{3} = \frac{y - 2}{5} = \frac{z - 3}{7},

is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 8th April 2017>Q 108

The line of intersection of the planes

\vec{r} \cdot (3 \hat{i} - \hat{j} + \hat{k}) = 1

and

\vec{r} \cdot (\hat{i} + 4 \hat{j} - 2 \hat{k}) = 2,

is,

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 9th April 2017>Q 109

If the line,

\frac{x - 3}{1} = \frac{y + 2}{- 1} = \frac{z + λ}{- 2}

lies in the plane,

2 x - 4 y + 3 z = 2

, then the shortest distance between this line and the line,

\frac{x - 1}{12} = \frac{y}{9} = \frac{z}{4}

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 9th April 2017>Q 110

If a variable plane, at a distance of

3

units from the origin, intersects the coordinate axes at

A, B & C

, then the locus of the centroid of

Δ A B C

is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 20 - Three Dimensional Geometry>JEE Main - 9th April 2016>Q 111

The shortest distance between the lines

\frac{x}{2} = \frac{y}{2} = \frac{z}{1}

and

\frac{x + 2}{- 1} = \frac{y - 4}{8} = \frac{z - 5}{4},

lies in the interval: