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If a line makes $α, β, γ, δ$ angles with four diagonals of a cube, then $\cos 2 α + \cos 2 β + \cos 2 γ + \cos 2 δ =$

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Important Questions on Three Dimensional Geometry

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 14 - Three Dimensional Geometry>Evaluation Test>Q 2

θ

is the acute angle between two intersecting straight lines, one having direction cosines

l_{1}, m_{1}, n_{1}

and the other having direction cosines

l_{2}, m_{2}, n_{2}

, then

\sin^{2} θ =

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 14 - Three Dimensional Geometry>Evaluation Test>Q 3

A (2, 3, 7), B (- 1, 3, 2), C (p, 5, r)

are vertices of

∆ A B C

. If the median through

A

is equally inclined to the co-ordinate axes, then the values of

p

and

r

are

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 14 - Three Dimensional Geometry>Evaluation Test>Q 4

A (3, 2, 6), B (1, 4, 5), C (3, 5, 3)

are the vertices of triangle

A B C

, then

m ∠ A B C =

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 14 - Three Dimensional Geometry>Evaluation Test>Q 5

The angle between the lines whose direction cosines are given by the equation

6 m n - 2 n l + 5 l m = 0, 3 l + m + 5 n = 0

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 14 - Three Dimensional Geometry>Evaluation Test>Q 6

l, m, n

are direction cosines of a line, then the maximum value of

l m + m n + n l

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 14 - Three Dimensional Geometry>Evaluation Test>Q 7

If the point

(a, 2, 3), (3, b, 7)

and

(- 3, - 2, - 5)

are collinear, the values of

a

and

b

, respectively are

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 14 - Three Dimensional Geometry>Evaluation Test>Q 8

The direction cosines of a line, which is perpendicular to both the lines whose direction ratios are

1, - 1, 0

and

2, - 1, 1

, are

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 14 - Three Dimensional Geometry>Evaluation Test>Q 9

Which of the following represents direction cosines of a line which is equally inclined to the axes?

If a line makes α, β, γ, δ angles with four diagonals of a cube, then cos2α+cos2β+cos2γ+cos2δ=

Important Questions on Three Dimensional Geometry

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If a line makes $α, β, γ, δ$ angles with four diagonals of a cube, then $\cos 2 α + \cos 2 β + \cos 2 γ + \cos 2 δ =$