# If a line makes angles 90°, 135°, 45° with the X-, Y- and Z-axes respectively, then find its direction cosines. - Mathematics and Statistics

Sum

If a line makes angles 90°, 135°, 45° with the X-, Y- and Z-axes respectively, then find its direction cosines.

#### Solution

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

Then l = cos α, m = cos β, n = cos γ

Here, α = 90°, β = 135°, γ = 45°

∴ l = cos 90° = 0

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

= - 1/sqrt2 and n = cos 45° = 1/sqrt2

∴ the direction cosines of the line are 0, - 1/sqrt2, 1/sqrt2

Concept: Vector Product of Vectors (Cross)
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