HARD

TS EAMCET

IMPORTANT

Earn 100

The combined equation for a pair of planes is $S \equiv 2 x^{2} - 6 y^{2} - 12 z^{2} + 18 y z + 2 z x + x y = 0 .$ If one of the planes is parallel to
$x + 2 y - 2 z = 5,$ then the acute angle between the planes $S = 0$ is

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Important Questions on Three Dimensional Geometry

MEDIUM

TS EAMCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Three Dimensional Geometry>TS EAMCET 2018 (04-May Shift-1)>Q 12

If the plane passing through the points

(1, 2, 3), (2, 3, 1)

and

(3, 1, 2)

a x + b y + c z = 1

then

a + 2 b + 3 c =

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Three Dimensional Geometry>TS EAMCET 2021 (04-Aug Shift-1)>Q 13

(\frac{9}{4}, \frac{5}{4}, \frac{15}{4})

is the centroid of a tetrahedron whose vertices are

(a, 2, 1), (1, b, 4),

(4, 0, c)

and

(1, 1, 7),

then

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Three Dimensional Geometry>TS EAMCET 2021 (04-Aug Shift-1)>Q 14

The point on the plane

2 x - 2 y + 4 z + 5 = 0

that is nearer to

(1, \frac{3}{2}, 2)

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Three Dimensional Geometry>TS EAMCET 2021 (04-Aug Shift-2)>Q 15

If a plane is at a distance of

6

units from the origin and the vector

2 \hat{i} + 6 \hat{j} - 3 \hat{k}

is its normal, then the equation of the plane in Cartesian form is

MEDIUM

TS EAMCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Three Dimensional Geometry>TS EAMCET - 5 August 2021 Shift 1>Q 16

The perpendicular distance from the origin to the plane containing the points having position vectors

\hat{i} + 2 \hat{j} + 3 \hat{k}, 2 \hat{i} + 3 \hat{j} - 4 \hat{k}, 3 \hat{i} - 4 \hat{j} + 5 \hat{k}

EASY

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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 17

A point on the plane determined by the points

A (1, 1, - 1), B (2, - 1, 0)

and

C (- 1, 0, 2)

among the following is

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Three Dimensional Geometry>TS EAMCET 2019 (03-May Shift-2)>Q 18

Vectors

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

are such that

(\vec{a} \times \vec{b}) \times (\vec{c} \times \vec{d}) = \vec{0} . P_{1}

and

P_{2}

are two planes determined by vectors

\bar{a}, \bar{b}

and

\bar{c}, \bar{d}

, respectively. Then the angle between the planes

P_{1}

and

P_{2}

HARD

TS EAMCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Three Dimensional Geometry>TS EAMCET 2019 (03-May Shift-2)>Q 19

π_{1}

is a plane passing through the point

(1, 2, 3)

and perpendicular to the planes

x + 2 y + 3 z - 6 = 0, x + 2 y + 2 z - 5 = 0

. If

(- 1, 2, - 3)

is the foot of the perpendicular drawn from the point

(1, 3, 2)

on to a plane

π_{2},

then the angle between the planes

π_{1}

and

π_{2}

The combined equation for a pair of planes is S≡2x2-6y2-12z2+18yz+2zx+xy=0. If one of the planes is parallel to x+2y-2z=5, then the acute angle between the planes S=0 is

Important Questions on Three Dimensional Geometry

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The combined equation for a pair of planes is $S \equiv 2 x^{2} - 6 y^{2} - 12 z^{2} + 18 y z + 2 z x + x y = 0 .$ If one of the planes is parallel to
$x + 2 y - 2 z = 5,$ then the acute angle between the planes $S = 0$ is