Question

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

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

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

(C) `1,1/sqrt2,1/sqrt2`

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

Answer 1

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

Let α, β, γ  be the angles made by the line with positive directions of X, Y, Z axes respectively.
α = 90°, β = 135°, γ = 45°
 l = cos 90°, m = cos 135°, n = cos 45°
Now, m = cos 135° = cos(180° – 45°)

=`-cos45^@=-1/sqrt2`

`l=0, m=-1/sqrt2, n=1/sqrt2`

Direction cosines of the line are   `0,-1/sqrt2,1/sqrt2`