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.

Answer 1

Angle made with $y$ axis $={45}^{\circ }=\beta$

Angle made with $z$ axis $={60}^{\circ }=\gamma$

Angle made with $x$ axis $=\alpha$

Since,

${\cos }^2\alpha +{\cos }^2\beta +{\cos }^2\gamma =1$

$⟹{\cos }^2\alpha +{\cos }^2{45}^{\circ }+{\cos }^2{60}^{\circ }=1$

$⟹co{s}^2\alpha +1=1$

$⟹co{s}^2\alpha =0$

$⟹\alpha ={90}^{\circ }$

Hence angle made with $x$ axis $={90}^{\circ }$.