Question

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

Options

• `0, 1/sqrt2, (-1)/sqrt2`

• `1/sqrt2, 0, 1/sqrt2`

• `(-1)/sqrt2, 1/sqrt2, sqrt3/2`

• `0, 1/sqrt2, sqrt3/2`

Answer 1

`0, 1/sqrt2, (-1)/sqrt2`

Explanation:

Line makes angles 90°, 45°, 135° with the X, Y and Z axes. Let l, m, n be d.c.s. of line given by l = cos α = cos 90° = 0,

m = cos β = cos 45° = `bar"AB"` and

n = cos γ = cos 135° = `bar"b"`.