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BITSAT 2021
Exam
BITSAT
Year
2021
Subject
Mathematics
Chapter
Three Dimensional Geometry

BITSAT 2021 · Mathematics · Three Dimensional Geometry

The length of the perpendicular drawn from the point (3,-1,11) to...

The length of the perpendicular drawn from the point (3,−1,11)(3,-1,11) to the line x2=y−23=z−34\frac{x}{2}=\frac{y-2}{3}=\frac{z-3}{4} is :

Options

  1. A29\sqrt{29}
  2. B33\sqrt{33}
  3. C53\sqrt{53}
  4. D66\sqrt{66}

Correct answer

C. 53\sqrt{53}

Step-by-step solution

Let feet of perpendicular is (2α,3α+2,4α+3)⇒(2 \alpha, 3 \alpha+2,4 \alpha+3)\Rightarrow Direction ratio of the ⊥\perp line is 2α−3,3α+3,4α−82 \alpha-3,3 \alpha+3,4 \alpha-8. and \Rightarrow Direction ratio of the line are 2,3,4⇒2(2α−3)+3(3α+3)+4(4α−8)=0⇒α=1⇒2,3,4\Rightarrow 2(2 \alpha-3)+3(3 \alpha+3)+4(4 \alpha-8)=0\Rightarrow \alpha=1\Rightarrow Feet of ⊥\perp is (2,5,7)⇒(2,5,7)\Rightarrow Length ⊥\perp is 12+62+42=53\sqrt{1^{2}+6^{2}+4^{2}}=\sqrt{53}
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