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

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If $A (3, 2, 3), B (1, 4, 6)$ 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 $D C$ 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 - 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 ∣ =

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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

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Three Dimensional Geometry>TS EAMCET - 5 August 2021 Shift 2>Q 29

The shortest distance between the Skew lines

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

and

\vec{r} = (\hat{i} - 7 \hat{j} - 2 \hat{k}) + μ (\hat{i} + 3 \hat{j} + 2 \hat{k})

is

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

If

(2, - 1, 2)

and

(K, - 3, - 5)

are the triads of direction ratios of two lines and the angle between the lines is

60 °,

then

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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 31

A line

L

is passing through the point

A

whose position vector is

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

and parallel to the vector

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

. A plane

π

is passing through the points

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

and parallel to the vector

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

. Then the point where this plane

π

meets the line

L

is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Three Dimensional Geometry>TS EAMCET - 5 August 2021 Shift 2>Q 32

\vec{a}, \vec{b}, \vec{c}

are non-coplanar vectors. If the position vector of the point of intersection of the line

\vec{r} = \vec{a} + 2 \vec{b} + p (\vec{a} - 2 \vec{c})

and the plane

\vec{r} = 3 \vec{a} - q (\vec{c} - \vec{b}) + k (\vec{a} - \vec{b} + \vec{c})

is

\vec{r} = x \vec{a} + y \vec{b} + z \vec{c},

then

x y z =