Question

A line lies in the XOZ plane and it makes an angle of 60° with the X-axis. Then its direction cosines are ______

Options

• `1/2, 0, sqrt3/2`

• `sqrt3/4, 0, 1/4`

• `0, 1/4, sqrt3/2`

• `1/2, 1/sqrt2,sqrt3/2`

Answer 1

A line lies in the XOZ plane and it makes an angle of 60° with the X-axis. Then its direction cosines are `underline(1/2, 0, sqrt3/2)`.

Explanation:

Since the line lies in the XOZ plane, therefore it is perpendicular to Y-axis.

∴ `beta = 90^circ` and it makes 60° angle with X-axis.

∴ cosβ = 0 and cosα = cos60°  = `1/2`

∴ cosΥ = cos(90° - 60°) = cos30° = `sqrt3/2`

∴ d.c.s. of given line are `1/2, 0, sqrt3/2`