MHT CET · Maths · Three Dimensional Geometry
If \(0 \equiv(0,0,0), \mathrm{P} \equiv(1, \sqrt{2}, 1)\), then the acute angles made by the line OP with XOY,
YOZ, ZOX planes are, respectively
- A \(45^{\circ}, 45^{\circ}, 60^{\circ}\)
- B \(45^{\circ}, 60^{\circ}, 30^{\circ}\)
- C \(60^{\circ}, 45^{\circ}, 60^{\circ}\)
- D \(30^{\circ}, 30^{\circ}, 45^{\circ}\)
Answer & Solution
Correct Answer
(D) \(30^{\circ}, 30^{\circ}, 45^{\circ}\)
Step-by-step Solution
Detailed explanation
Direction ratios of line OP are \(1, \sqrt{2}, 1\).
Hence direction cosines of line OP are
\(\frac{1}{\sqrt{1+2+1}}, \frac{\sqrt{2}}{\sqrt{1+2+1}}, \frac{1}{\sqrt{1+2+1}}=\frac{1}{2}, \frac{1}{\sqrt{2}}, \frac{1}{2}\)
Hence angles made with given planes are \(60^{\circ}, 45^{\circ}, 60^{\circ}\)
Hence direction cosines of line OP are
\(\frac{1}{\sqrt{1+2+1}}, \frac{\sqrt{2}}{\sqrt{1+2+1}}, \frac{1}{\sqrt{1+2+1}}=\frac{1}{2}, \frac{1}{\sqrt{2}}, \frac{1}{2}\)
Hence angles made with given planes are \(60^{\circ}, 45^{\circ}, 60^{\circ}\)
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