Question

If a line makes angles ${45}^{\circ },{60}^{\circ }$ and ${60}^{\circ }$ with the positive direction of $x,y,z-\text{axes}$ respectively, then its direction cosines are ________

Answer 1

The direction cosines of a line which makes angles $\alpha ,\beta ,\gamma$ with the axes, are $\cos \alpha ,\cos \beta ,\cos \gamma$.

$\therefore$ D.C.'s of the given line are $\cos {45}^{\circ },\cos {60}^{\circ }$ and $\cos {60}^{\circ }$ i.e., $(\frac{1}{\sqrt{2}},\frac{1}{2},\frac{1}{2})$