Question

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

Answer 1

It is given that the angles which lines makes are 90° with respect to x-axis, 135°with respect to y-axis and 45° with respect to z-axis.

Let the direction cosine of the line be l,m,n.

Direction cosine of line l is,

l=cos90° l=0

Direction cosine of line m is,

m=cos135° m=−cos45° m= −1 2

Direction cosine of line n is,

n=cos45° n= 1 2

Thus, the direction cosines are 0, −1 2 and 1 2 .