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The direction cosines of a line that are perpendicular to the lines with direction ratios $4, 1, 3$ and $2, - 3, 1$ are

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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>Competitive Thinking>Q 1

α, β, γ

be the angles which a line makes with the coordinate axes, then

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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>Competitive Thinking>Q 2

\cos α, \cos β, \cos γ

are the direction cosines of a vector

\vec{a},

then

\cos 2 α + \cos 2 β + \cos 2 γ

is equal to

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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>Competitive Thinking>Q 3

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

are the direction cosines of a line then the value of

n

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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>Competitive Thinking>Q 4

If the direction cosines of a line are

\frac{1}{c}, \frac{1}{c}, \frac{1}{c}

, then

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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>Competitive Thinking>Q 5

A line

A B

in three-dimensional space makes angles

45 °

and

120 °

with the positive

X -

axis and the positive

Y -

axis respectively. If

A B

makes an acute angle

θ

with the positive

Z -

axis, then

θ

equals

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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>Competitive Thinking>Q 6

If a line makes angles

120 °

and

60 °

with the positive directions of

X

and

Z -

axes, respectively, then the angle made by the line with positive

Y -

axis is

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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>Competitive Thinking>Q 7

If a line makes an angle of

\frac{π}{4}

with the positive directions of each of

X

-axis and

Y

-axis, then the angle that the line makes with the positive direction of the

Z

-axis is

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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>Competitive Thinking>Q 8

If a vector

\vec{x}

makes angles with measure

\frac{π}{4}

and

\frac{5 π}{4}

with positive directions of

X -

axis and

Y -

axis respectively. Then

\vec{x}

made angle of measure _______ with positive direction of

Z -

axis

The direction cosines of a line that are perpendicular to the lines with direction ratios 4, 1, 3 and 2, -3, 1 are

Important Questions on Three Dimensional Geometry

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The direction cosines of a line that are perpendicular to the lines with direction ratios $4, 1, 3$ and $2, - 3, 1$ are