If a line makes angles 90°, 135°, 45° with the x, y and z-axes respectively, find its direction cosines.

Required direction cosines are either
$< cos90^\circ ,cos135^\circ ,cos45^\circ >$

or $< - cos90^\circ , - cos135^\circ , - cos45^\circ >$

i.e., either $< 0, - \cfrac{1}{{\sqrt 2 }},\cfrac{1}{{\sqrt 2 }} >$ or $< 0,\cfrac{1}{{\sqrt 2 }}, - \cfrac{1}{{\sqrt 2 }} >$