Gamma Question Bank for Engineering Mathematics>Chapter 16 - Introduction to Three Dimensional Geometry>Assignment>Q 30

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The points $(8, - 5, 6), (11, 1, 8), (9, 4, 2)$ and $(6, - 2, 0)$ are vertices of a cyclic quadrilateral and its area is $k$ sq. units, then the value of $k$ is

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Important Questions on Introduction to Three Dimensional Geometry

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Gamma Question Bank for Engineering Mathematics>Chapter 16 - Introduction to Three Dimensional Geometry>Assignment>Q 31

There area of the triangle whose vertices are the points

(2, 1, 1), (3, 1, 2), (- 4, 0, 1)

is

λ

square units then

{(2 λ)}^{2}

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 16 - Introduction to Three Dimensional Geometry>Assignment>Q 32

If

α, β, γ

are the angle made by line joining points

A (3, 5, - 2)

and

B (- 1, 3, - 4)

then the value of

{(\cos 2 α + \cos 2 β + \cos 2 γ)}^{2} + 3 (\sin^{2} α + \sin^{2} β + \sin^{2} γ)

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 16 - Introduction to Three Dimensional Geometry>Assignment>Q 33

The sum of values of

λ

, for which the triangle with vertices

(6, 10, 10), (1, 0, - 5)

and

(6, - 10, λ)

will be right-angled is

k

, then

3 k

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 16 - Introduction to Three Dimensional Geometry>Assignment>Q 34

The distance of point

P (5, - 7, - 6)

, from the point

Q

which divides line segment joining points

A (- 2, 3, 5)

and

B (7, 0, - 1)

in ratio

1 : 2

internally is

λ

then

λ^{2}

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 16 - Introduction to Three Dimensional Geometry>Assignment>Q 2

If the extremities of the diagonal of a square are

(1, - 2, 3)

and

(3, - 4, 3)

, then the length of the side is

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Gamma Question Bank for Engineering Mathematics>Chapter 16 - Introduction to Three Dimensional Geometry>Assignment>Q 3

If origin is the centroid of the triangle with vertices

P (3 a, 3, 6), Q (- 4, 2 b, - 8)

and

R (8, 12, 2 c)

, then the value of

a, b

and

c

are

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Gamma Question Bank for Engineering Mathematics>Chapter 16 - Introduction to Three Dimensional Geometry>Assignment>Q 4

If the three vertices of a parallelogram

A B C D

are

A (3, - 1, 5), B (1, - 2, - 4)

and

C (0, 3, 0)

, then the coordinates of fourth vertex is

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Gamma Question Bank for Engineering Mathematics>Chapter 16 - Introduction to Three Dimensional Geometry>Assignment>Q 5

The ratio in which the join of

A (1, 2, 3)

and

B (3, 4, 6)

is divided by

X Y

plane externally is