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Three Dimensional Geometry

Question
CBSEENMA12036178
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If a line makes an angle of 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

  • π/6

  • π/3

  • π/4

  • π/2

Solution

D.

π/2

l = cos π/4 , m = cos π/4
we know l2 + m2 + n2 = 1
1 half space plus space 1 half space plus straight n squared space equals 1 rightwards double arrow space straight n space equals space 0
Hence angle with the positive direction of z-axis is π/2 .

Some More Questions From Three Dimensional Geometry Chapter

If α, β, γ are the angles which a line makes with the axes, prove that sin2α + sin2 β + sin2γ = 2.

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