JEE Mains · Maths · STD 12 - 11. three dimension geometry
The line \(L_1\) is parallel to the vector \(\vec{a}=-3 \hat{i}+2 \hat{j}+4 \hat{k}\) and passes through the point \((7,6,2)\) and the line \(L_2\) is parallel to the vector \(\vec{b}=2 \hat{i}+\hat{j}+3 \hat{k}\) and passes through the point \((5,3,4)\). The shortest distance between the lines \(L_1\) and \(L_2\) is :
- A \(\frac{23}{\sqrt{38}}\)
- B \(\frac{21}{\sqrt{57}}\)
- C \(\frac{23}{\sqrt{57}}\)
- D \(\frac{21}{\sqrt{38}}\)
Answer & Solution
Correct Answer
(A) \(\frac{23}{\sqrt{38}}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & L_1:(7 \hat{i}+6 \hat{j}+2 k)+\lambda(-3 \hat{i}+2 \hat{j}+4 k) \\ & L_2:(5 \hat{i}+3 \hat{j}+4 k)+\lambda(2 \hat{i}+\hat{j}+3 k)\end{aligned}\) Distance between skew lines…
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