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# If a line makes angles $90^{\circ}, 135^{\circ}, 45^{\circ}$ with the x, y and z axes respectively, find its direction cosines.

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• The cosine of the angles made by the directed line, passing through the origin with the x,y and z axes are called direct cosines.
Given :
$\alpha =90^{\circ},\:\:\beta=135^{\circ}\:\:and\:\:\gamma=45^{\circ}$
The direction cosines are
$\cos \alpha =\cos 90^{\circ}=0$
$\cos \beta =\cos 135^{\circ}=\cos(180^{\circ}-45^{\circ})$
$\qquad\qquad\quad\quad\;\;\;=\large\frac{-1}{\sqrt 2}$
$\cos \gamma =\cos 45^{\circ}=1$
Hence the direction cosines are $(0,\large\frac{-1}{\sqrt 2}$$,1)$