The distance between parallel lines $\frac{x-1}{2}=\frac{y-2}{-2}=\frac{z-3}{1}$ and…

The distance between parallel lines $\frac{x-1}{2}=\frac{y-2}{-2}=\frac{z-3}{1}$ and $\frac{x}{2}=\frac{y}{-2}=\frac{z}{1}$ is
  1. $\frac{2 \sqrt{5}}{3}$ units
  2. $\frac{5 \sqrt{5}}{3}$ units
  3. $\frac{\sqrt{5}}{3}$ units
  4. $\frac{4 \sqrt{5}}{3}$ units

Solution

$\begin{aligned} & \Rightarrow \text { S.D. }=\frac{|8 \hat{i}+5 \hat{j}-6 \hat{k}|}{\sqrt{9}} \\ & \Rightarrow \text { S.D. }=\frac{\sqrt{8^2+5^2+(-6)^2}}{3} \\ & \Rightarrow \text { S.D. }=\frac{\sqrt{125}}{3}=\frac{5 \sqrt{5}}{3} \\ & \end{aligned}$

Asked in: MHT CET 2022 (06 Aug Shift 2)

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