EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Three Dimensional Geometry>AP EAPCET 2019 (21-Apr Shift-2)>Q 14

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The equation of the plane in normal form which passes through the points $(- 2, 1, 3), (1, 1, 1)$ and $(2, 3, 4)$ is

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Important Questions on Three Dimensional Geometry

HARD

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Three Dimensional Geometry>AP EAPCET 2018 (25-APR Shift-1)>Q 15

A plane passes through the point

(3, 5, 7)

. If the direction ratios of its normal are equal to the intercepts made by the plane

x + 3 y + 2 z = 9

with the coordinate axes, then the equation of that plane is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Three Dimensional Geometry>AP EAPCET - 20 Aug 2021 Afternoon>Q 16

The sum of intercepts of the plane

4 x + 3 y + 2 z = 2

on the coordinate axes is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Three Dimensional Geometry>AP EAPCET 2021 (19-Aug Afternoon)>Q 17

X

intercept of the plane containing the line of intersection of the planes

x - 2 y + z + 2 = 0

and

3 x - y - z + 1 = 0

and also passing through

(1, 1, 1)

is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Three Dimensional Geometry>AP EAPCET 2021 (19-Aug Afternoon)>Q 18

Find the equation of the plane passing through the point

(2, 1, 3)

and perpendicular to the planes

x - 2 y + 2 z + 3 = 0

and

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

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Three Dimensional Geometry>AP EAPCET - 20 Aug 2021 Forenoon>Q 19

Let $\vec{a} = \hat{i}$ and $\vec{b} = \hat{j}$ is the point of intersection of the lines $\vec{r} \times \vec{a} = \vec{b} \times \vec{a}$ and $\vec{r} \times \vec{b} = \vec{a} \times \vec{b}$ is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Three Dimensional Geometry>AP EAPCET 2020 (Sep-23 Shift-1)>Q 20

If

(a_{1}, b_{1}, c_{1}), (a_{2}, b_{2}, c_{2})

are the direction cosines of two lines making an angle

θ

with each other, then

\cos θ =

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Three Dimensional Geometry>AP EAPCET 2019 (21-Apr Shift-2)>Q 21

The angle between a line with direction ratios

2, 2, 1

and the line joining the points

(3, 1, 4)

and

(7, 2, 12)

is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Three Dimensional Geometry>AP EAPCET 2021 (19-Aug Afternoon)>Q 22

Let

L_{1}

(respectively

L_{2}

) be the line passing through

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

(respectively

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

) and parallel to

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

(respectively

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

). Then the shortest distance between the lines

L_{1}

and

L_{2}

is equal to