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

1. 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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Let the direction cosines of the line be l,m, and n.

So, we have

l = \cos90^{\circ}=0       

m = \cos135^{\circ}=-\frac{1}{\sqrt2}

n= \cos45^{\circ}=\frac{1}{\sqrt2}

Therefore the direction cosines of the lines are 0,\ -\frac{1}{\sqrt2},and\ \ \frac{1}{\sqrt2}.

Posted by

Divya Prakash Singh

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