EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Three Dimensional Geometry>TS EAMCET 2020 (9-Sep Shift-1)>Q 7

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IMPORTANT

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If $l, m, n$ are the direction cosines of a line which makes angles $α, β$ and $γ$ with the coordinate axes $X, Y, Z$ , respectively, then $l m + m n + n l$ takes the maximum value when

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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 8

The lines whose direction cosines are given by the relations

a l + b m + c n = 0

and

m n + n l + l m = 0

are

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 9

The direction cosines of the line making angles

\frac{π}{4}, \frac{π}{3}

and

θ (0 < θ < \frac{π}{2})

respectively with

x, y

and

z

axes, are

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 10

The direction cosines of the line passing through

P (2, 3, - 1)

and the origin are

HARD

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Three Dimensional Geometry>TS EAMCET 2020 (9-Sep Shift-1)>Q 11

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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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)

is

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

If

(\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)

is

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