A line makes angles of 45° and 60° with the positive axes of X and Y respectively. The angle made by the same line with the positive axis of Z, is.

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A line makes angles of 45° and 60° with the positive axes of X and Y respectively. The angle made by the same line with the positive axis of Z, is.

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90°or120°

30°or 60°

60° or 90 $°$

60°or l20°

answer is D.

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Detailed Solution

Given $α = 45^{\circ}, β = 60^{\circ}, γ = ?$

$\begin{array}{l} ∵ \cos^{2} α + \cos^{2} β + \cos^{2} γ = 1 \\ ∴ \cos^{2} γ = 1 - \frac{1}{2} - \frac{1}{4} = \frac{1}{4} \Rightarrow γ = 60^{\circ} or 120^{\circ} \end{array}$

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