Question

If a line makes an angle of 90°, 60°, 30° with the positive direction of
x, y, z-axis, respectively, then find its direction cosines.

• A. (0,2,1)
• B. $\left(0,\frac{1}{2},\frac{\sqrt{3}}{2}\right)$
• C. $\left(\frac{1}{2},0,\frac{\sqrt{3}}{2}\right)$
• D.
  $\left(0,\frac{1}{2},\frac{3}{2}\right)$

Answer 1

The correct option is B $\left(0,\frac{1}{2},\frac{\sqrt{3}}{2}\right)$

The direction cosines of a line which makes an angle of $\alpha ,\beta ,\gamma$ with the axis,
are cos$\alpha$, cos$\beta$, cos$\gamma$
Therefore, D.C.’s of the line are cos90°, cos60°, cos30° i.e.,$\left(0,\frac{1}{2},\frac{\sqrt{3}}{2}\right)$