Question

If a line makes angles 120° and 60° with the positive directions of X and Z axes respectively then the angle made by the line with positive Y-axis is ______.

Options

• 150°

• 60°

• 135°

• 120°

Answer 1

If a line makes angles 120° and 60° with the positive directions of X and Z axes respectively then the angle made by the line with positive Y-axis is 135°.

Explanation:

Let cos α, cos β and cos γ are the direction cosines of the line.

We know that cos² α, cos² β + cos² γ = 1

`\implies` (cos 120°)²  + cos² β + (cos 60°)² = 1

`\implies (-1/2)^2 + cos^2 β + (1/2)^2` = 1

`\implies` cos² β = `1 - 1/2 = 1/2`

`\implies` cos β = `± 1/sqrt(2)`

`\implies` β = 135°