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Three Dimensional Geometry — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsThree Dimensional Geometry1 Mark
MCQ
A line with positive direction cosines passes through the point P(2, -1, 2) and makes equal angles with the coordinate axes. The line meets the plane 2x + y + z = 9 at point Q. The length of the line segment PQ equals:
  • A
    $1$
  • B
    $\sqrt{2}$
  • C
    $\sqrt{3}$
  • D
    $2$
✓

Answer

  1. $\sqrt{3}$

Solution:

D.C of the line are $\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}$

Any point on the line at a distance tt from P(2, -1, 2) is

$\Big(2+\frac{\text{t}}{\sqrt{3}},-1+\frac{\text{t}}{\sqrt{3}},2+\frac{\text{t}}{\sqrt{3}}\Big)$

which lies on $2\text{x} + \text{y + z} = 9$

$\Rightarrow\text{t}=\sqrt{3}$

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