EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Three Dimensional Geometry>TS EAMCET 2018 (04-May Shift-1)>Q 2

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Assertion $(A)$ : If $(- 1, 3, 2)$ and $(5, 3, 2)$ are respectively the orthocentre and circumcentre of a triangle, then $(3, 3, 2)$ is its centroid.

Reason $(R)$ : Centroid of the triangle divides the line segment joining the orthocentre and the circumcentre in the ratio $1 : 2$ .

Which one of the following is true?

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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 3

If the mid points of the sides

A B, B C

and

C A

of a triangle are respectively

D (1, 2, - 3),

E (3, 0, 1)

and

F (- 1, 1, - 4),

then the centroid of the triangle

A D F

is

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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 4

The position vectors of the points

P

and

Q

are respectively

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

and

3 \bar{i} + 3 \bar{j} + 2 \bar{k} .

The ratio in which the point having position vector

\frac{- 9}{2} \bar{i} - 6 \bar{j} + \frac{1}{2} \bar{k}

divides the line segment joining

P

and

Q

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 5

If the collinear points

A, B

and

C

have position vectors respectively

(1, x, 3), (3, 4, 7)

and

(y, - 2, - 5),

then

x + y =

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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 6

The centroid of a triangle with vertices

A (3, 4, 5), B (6, 7, 2)

and

C (x, y, z)

is

(3, 2, 3)

then

x + y + z =

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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 7

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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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

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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

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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 10

The direction cosines of the line passing through

P (2, 3, - 1)

and the origin are