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Q.

If a line makes an angle of π4 with the positive direction 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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a

π3

b

π4

c

π2

d

π6

answer is C.

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Detailed Solution

Here l=cos⁡π4,m=cos⁡π4Let the line make an angle  γ with the z-axis. Then l2+m2+n2=1or  cos2⁡π4+cos2⁡π4+cos2⁡γ=1or  12+12+cos2⁡γ=1or  2cos2⁡γ=0 or cos⁡γ=0 or γ=π2
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