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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