CUET · MATHS · PYQ PAPER 2023
If a line makes angles \(90^{\circ}, 60^{\circ}\) and \(\theta\) with x, y and z axis respectively, where \(\theta\) is acute, then value of \(\theta\) is :
- A \(\frac{\pi}{6}\)
- B \(\frac{\pi}{4}\)
- C \(\frac{\pi}{3}\)
- D \(\frac{\pi}{2}\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{6}\)
Step-by-step Solution
Detailed explanation
\(\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1\) \(\cos^2 90^{\circ} + \cos^2 60^{\circ} + \cos^2 \theta = 1\) \(0^2 + \left(\frac{1}{2}\right)^2 + \cos^2 \theta = 1\) \(0 + \frac{1}{4} + \cos^2 \theta = 1\) \(\cos^2 \theta = 1 - \frac{1}{4}\) \(\cos^2 \theta = \frac{3}{4}\)…
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