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Question

A line makes angles of measure $$45^{\circ}$$ and $$60^{\circ}$$ with the positive direction of the Y and Z axes respectively. Find the angle made by line with the positive directions of X-axis.


Solution

Angle made with $$y$$ axis $$=45^\circ=\beta$$
Angle made with $$z$$ axis $$=60^\circ=\gamma$$
Angle made with $$x$$ axis $$=\alpha$$
Since, 
$$\cos^2\alpha+\cos^2\beta+\cos^2\gamma=1$$
$$\implies \cos^2\alpha+\cos^2 45^\circ+\cos^260^\circ=1$$
$$\implies cos^2\alpha+1=1$$
$$\implies cos^2\alpha=0$$
$$\implies \alpha=90^\circ$$
Hence angle made with $$x$$ axis $$=90^\circ$$.

Mathematics

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