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Question: Answered & Verified by Expert
The shortest distance between the lines $\frac{x-3}{3}=\frac{y-8}{-1}=\frac{z-3}{1}$ and $\frac{x+3}{-3}=\frac{y+7}{2}=\frac{z-6}{4}$ is
MathematicsThree Dimensional GeometryMHT CETMHT CET 2022 (11 Aug Shift 1)
Options:
  • A $2 \sqrt{30}$ units
  • B $\sqrt{30}$ units
  • C $4 \sqrt{30}$ units
  • D $3 \sqrt{30}$ units
Solution:
2653 Upvotes Verified Answer
The correct answer is: $3 \sqrt{30}$ units
$\begin{aligned} & \text { Shortest distance }=\left|\frac{\left|\begin{array}{ccc}3-(-3) & 8-(-7) & 3-6 \\ 3 & -1 & 1 \\ -3 & 2 & 4\end{array}\right|}{\sqrt{(-4-2)^2+(12+3)^2+(6-3)^2}}\right| \\ & =\frac{|6 \times(-6)-15 \times(15)-3 \times(3)|}{\sqrt{36+225+9}} \\ & =\frac{270}{\sqrt{270}}=\sqrt{270}=3 \sqrt{30}\end{aligned}$

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