MHT CET · Maths · Three Dimensional Geometry
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
- A \(\frac{2 \sqrt{5}}{3}\) units
- B \(\frac{5 \sqrt{5}}{3}\) units
- C \(\frac{\sqrt{5}}{3}\) units
- D \(\frac{4 \sqrt{5}}{3}\) units
Answer & Solution
Correct Answer
(B) \(\frac{5 \sqrt{5}}{3}\) units
Step-by-step Solution
Detailed explanation
\(\Rightarrow \text { S.D. }=\frac{|8 \hat{i}+5 \hat{j}-6 \hat{k}|}{\sqrt{9}}\)
\(\Rightarrow \text { S.D. }=\frac{\sqrt{8^2+5^2+(-6)^2}}{3}\)
\(\Rightarrow \text { S.D. }=\frac{\sqrt{125}}{3}=\frac{5 \sqrt{5}}{3}\)
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