MHT CET · Maths · Three Dimensional Geometry
If a line makes angles of measure \(\frac{\pi}{6}\) and \(\frac{\pi}{3}\) with \(\mathrm{X}\) and Y axes respectively, then the angle made by the line with \(\mathrm{Z}\) axis is
- A \(\frac{\pi}{6}\)
- B \(\frac{\pi}{2}\)
- C \(\cdot \frac{\pi}{4}\)
- D \(\frac{\pi}{5}\)
Answer & Solution
Correct Answer
(B) \(\frac{\pi}{2}\)
Step-by-step Solution
Detailed explanation
Let the line make an angle \(\theta\) with \(Z\) axis.
\(\begin{array}{l}\therefore \cos ^{2} \frac{\pi}{6}+\cos ^{2} \frac{\pi}{3}+\cos ^{2} \theta=1 \\\therefore \cos ^{2} \theta=1-\left(\frac{3}{4}+\frac{1}{4}\right)=0 \Rightarrow \theta=\frac{\pi}{2}\end{array}\)
\(\begin{array}{l}\therefore \cos ^{2} \frac{\pi}{6}+\cos ^{2} \frac{\pi}{3}+\cos ^{2} \theta=1 \\\therefore \cos ^{2} \theta=1-\left(\frac{3}{4}+\frac{1}{4}\right)=0 \Rightarrow \theta=\frac{\pi}{2}\end{array}\)
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