EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Three Dimensional Geometry>AMU-AT (B.Tech.) 2018>Q 5

MEDIUM

AMU-AT (B.Tech.)

IMPORTANT

Earn 100

The length of perpendicular from the point $\hat{i} + 2 \hat{j} + 3 \hat{k}$ to the line $\frac{x - 6}{3} = \frac{y - 7}{2} = \frac{z - 7}{- 2}$ is

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Important Questions on Three Dimensional Geometry

EASY

AMU-AT (B.Tech.)

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Three Dimensional Geometry>AMU-AT (B.Tech.) 2018>Q 6

The angle between the line

x - 2 y + z = 0 = x + 2 y - 2 z

and the plane

5 x - 2 y - z + 17 = 0

is

MEDIUM

AMU-AT (B.Tech.)

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Three Dimensional Geometry>AMU-AT (B.Tech.) 2018>Q 7

The distance of point of intersection of the line

\frac{x - 2}{3} = \frac{y + 1}{4} = \frac{z - 2}{12}

with the plane

x - y + z = 5

from the point with position vector

\hat{i} - 2 \hat{j} + 3 \hat{k}

is

MEDIUM

AMU-AT (B.Tech.)

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Three Dimensional Geometry>AMU-AT (B.Tech.) 2017>Q 8

The shortest distance between the lines

\vec{r} = (4 \hat{i} - \hat{j}) + λ (\hat{i} + 2 \hat{j} - 3 \hat{k})

and

\vec{r} = (\hat{i} - \hat{j} + 2 \hat{k}) + μ (2 \hat{i} + 4 \hat{j} - 5 \hat{k})

is

MEDIUM

AMU-AT (B.Tech.)

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 28 - Three Dimensional Geometry>AMU-AT (B.Tech.) 2017>Q 9

Let

A

and

B

be two points with position vectors

\vec{a}

and

\vec{b}

respectively and let

C

be a point dividing

A B

internally and the position vector of

C

on

A B

is

\vec{c} = λ \vec{a} + μ \vec{b},

then