Question

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

Answer 1

Let the direction cosines of a line from x,yand z axes be l, m and n respectively. Given, `alpha = 90^(@), beta = 135^(@)` and `gamma = 45^(@)`
Therefore, `l = cos , alpha = cos 90^(@) = 0`,
`m = cos beta = cos 135^(@) = - 1//2`
and `n = cos gamma = cos 45^(@) = 1//sqrt(2)`
Therefore, direction cosines of the lines are `0, - (1)/(sqrt(2))` and `(1)/(sqrt(2))`.