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

Let the direction cosines of the line making ∠ α with x-axis, β – with y axis and γ- with z axis are l, m and n

⇒ l = cos α, m = cos β and n = cos γ

Here α = 90°, β = 135° and γ = 45°

So direction cosines are

l = cos 90° = 0

m = cos 135°= cos (180° - 45°) = -cos 45° =

n = cos 45° =

⇒ Direction cosines of the line

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