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  • If the line OP makes with the x-axis an angle of measure 120 degree and with y-axis is 60. Find angle made by line with z axis

If the line OP makes with the x-axis an angle of measure 120 degree and with y-axis is 60. Find angle made by line with z axis.

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\\\text{We know that } \cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} Y=1 \\ \text{ i.e., sum of the squares of the direcction cosines is unity, } \\ \text{Where } \alpha, \beta, \gamma \text{ are the angles made by a line with positive direction of the axes, }

\\\Longrightarrow \frac{1}{4}+\cos ^{2} \beta+\frac{1}{4}=1 \\ \Longrightarrow \cos ^{2} \beta=\frac{1}{2} \\ \cos \beta=\frac{1}{\sqrt{2}} or -\frac{1}{\sqrt{2}} \\\\ \Longrightarrow \beta=45^{0} or 135^{0}

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