The two lines L 1 : r → = ( i ^ + 5 j ^ + 5 k ^ ) + t ( 4 i ^ - 4 j ^ + 5 k ^ ) and L 2 : r → = ( 2 i ^ + 4 j ^ + 5 k ^ ) + s ( 8 i ^ - 3 j ^ + k ^ ) are such that

both are non-Skew lines, non-parallel, non-perpendicular

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The vector in the direction of the sum of the vectors $\vec{a} = 2 \hat{i} - 2 \hat{j} + 5 \hat{k} and \vec{b} = - 2 \hat{i} + 5 \hat{j} - 3 \hat{k}$ is

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Important Questions on Three Dimensional Geometry

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Three Dimensional Geometry>TS EAMCET 2021 (04-Aug Shift-2)>Q 21

A plane

a x + b y + c z + 1 = 0

is perpendicular to the two planes

2 x - 2 y + z = 0

and

x - y + 2 z = 4

and passes through the point

(1, - 2, 1)

. Then

a + b - c =

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Three Dimensional Geometry>TS EAMCET - 5 August 2021 Shift 1>Q 22

The Cartesian equation of a plane parallel to the plane

\vec{r} \cdot (2 \hat{i} + 3 \hat{j} - 4 \hat{k}) = 1

and at a distance of

2

units from it is

HARD

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Three Dimensional Geometry>TS EAMCET 2018 (04-May Shift-1)>Q 23

Let

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

be the position vector of a point

B

. Let

A

be a point on the line which is passing through

B

and parallel to the vector

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

. If

|\vec{B A}| = 18

, then the position vector of

A

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Three Dimensional Geometry>TS EAMCET 2018 (04-May Shift-1)>Q 24

If the position vectors of three points

A, B, C

respectively are

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

and

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

, then the perpendicular distance of the point

C

from the line

A B

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Three Dimensional Geometry>TS EAMCET 2019 (03-May Shift-2)>Q 25

\vec{r} = \hat{i} + \hat{j} + t (2 \hat{i} - \hat{j} + \hat{k})

and

\vec{r} = 2 \hat{i} - \hat{j} - \hat{k} + t (3 \hat{i} - 5 \hat{j} + 2 \hat{k})

are the vector equations of two lines

L_{1}

and

L_{2}

then the shortest distance between them is

MEDIUM

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Three Dimensional Geometry>TS EAMCET 2019 (03-May Shift-2)>Q 26

A (3, 2, 3), B (1, 4, 6)

and

C (7, 4, 5)

are the three vertices of a parallelogram

A B C D

, then the angle between its diagonal through

D

and the side

D C

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Three Dimensional Geometry>TS EAMCET - 5 August 2021 Shift 1>Q 27

Suppose

L_{1}

and

L_{2}

are two lines having the direction ratios

1, - 2, - 2

and

0, 2, 1

respectively. If the direction cosines of a line perpendicular to both

L_{1}

and

L_{2}

are

l, m, n

then

|l| + | m | + | n ∣ =

MEDIUM

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Three Dimensional Geometry>TS EAMCET - 5 August 2021 Shift 2>Q 28

The two lines

L_{1} : \vec{r} = (\hat{i} + 5 \hat{j} + 5 \hat{k}) + t (4 \hat{i} - 4 \hat{j} + 5 \hat{k})

and

L_{2} : \vec{r} = (2 \hat{i} + 4 \hat{j} + 5 \hat{k}) + s (8 \hat{i} - 3 \hat{j} + \hat{k})

are such that

The vector in the direction of the sum of the vectors a→=2i^-2j^+5k^ and b→=-2i^+5j^-3k^ is

Important Questions on Three Dimensional Geometry

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The vector in the direction of the sum of the vectors $\vec{a} = 2 \hat{i} - 2 \hat{j} + 5 \hat{k} and \vec{b} = - 2 \hat{i} + 5 \hat{j} - 3 \hat{k}$ is