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Question
If a line is inclined at 60° and 30° with the X and Y-axes respectively, then the angle which it makes with Z-axis is
(A) 0
(B) `pi/4`
(C) `pi/2`
(D) `pi/6`
Solution
Let α, β, γ be the angles made by a line with X, Y, Z axes respectively
∴ α = 60°, β = 30°
Since, cos2α + cos2β + cos2γ = 1
∴ cos2 60° + cos2 30° + cos2 γ = 1
∴ `1/4 + 3/4 + cos^2 gamma = 1`
∴ `gamma = pi/2`
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