JEE Main 2025 (Online) 2nd April Evening ShiftQuestion 1
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 :
3D Geometry
Solution
$\vec a\times\vec b=(2,17,-7)$, $|\cdot|=\sqrt{342}=3\sqrt{38}$. Joining vector $(-2,-3,2)$, dot $=-69$. Distance $=\frac{69}{3\sqrt{38}}=\frac{23}{\sqrt{38}}$.