Q 1461634525.     Find the angles which the vector `vec{i}- vec{j}+ sqrt{2} vec{k}` makes with the coordinate axes.

A

`frac{ pi}{3}, frac{2 pi}{5}, frac{ pi}{5}`

B

`frac{ pi}{3}, frac{ pi}{3}, frac{ pi}{4}`

C

`frac{ pi}{ sqrt 2}, frac{2 pi}{3}, frac{ pi}{2}`

D

`frac{ pi}{3}, frac{2 pi}{3}, frac{ pi}{4}`

HINT

The direction cosines of vector `vec a=a_1 vec i+a_2 vec j+a_3 vec k` are `l = frac{a_1}{| vec a|}, m = frac{a_2}{| vec a|}, n = frac{a_3}{| vec a|}`. The angles made by `vec a` with the coordinate axes are `cos^{-1}l, cos^{-1}m,

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