If $0 \equiv(0,0,0), \mathrm{P} \equiv(1, \sqrt{2}, 1)$, then the acute angles made by the line OP with XOY,…
If $0 \equiv(0,0,0), \mathrm{P} \equiv(1, \sqrt{2}, 1)$, then the acute angles made by the line OP with XOY,
YOZ, ZOX planes are, respectively
$45^{\circ}, 45^{\circ}, 60^{\circ}$
$45^{\circ}, 60^{\circ}, 30^{\circ}$
$60^{\circ}, 45^{\circ}, 60^{\circ}$
$30^{\circ}, 30^{\circ}, 45^{\circ}$
Solution
Direction ratios of line OP are $1, \sqrt{2}, 1$.
Hence direction cosines of line OP are
$\frac{1}{\sqrt{1+2+1}}, \frac{\sqrt{2}}{\sqrt{1+2+1}}, \frac{1}{\sqrt{1+2+1}}=\frac{1}{2}, \frac{1}{\sqrt{2}}, \frac{1}{2}$
Hence angles made with given planes are $60^{\circ}, 45^{\circ}, 60^{\circ}$