Q98 / 180 · KCET 2025 · Mathematics

If a line makes angles $90^{\circ}, 60^{\circ}$ and $\theta$ with $\mathrm{x}, \mathrm{y}$ and z axes respectively, where $\theta$ is acute, then the value of $\theta$ is

  • Correct answer
    A
    $\frac{\pi}{6}$
  • B
    $\frac{\pi}{4}$
  • C
    $\frac{\pi}{3}$
  • D
    $\frac{\pi}{2}$

Solution

$\begin{aligned} & \ell^2+\mathrm{m}^2+\mathrm{n}^2=1 \\ & \mathrm{n}^2=1-\frac{1}{4} \Rightarrow \mathrm{n}=\frac{\sqrt{3}}{2}\end{aligned}$

Hence, the correct answer is option: 'A'.

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