Q81 / 150 · MHT CET 2020 (12 Oct Shift 1) · Mathematics

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
    $60^{\circ}, 45^{\circ}, 60^{\circ}$
  • Correct answer
    D
    $30^{\circ}, 30^{\circ}, 45^{\circ}$

Solution

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, the correct answer is option: 'D'.

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