JEE Main 2025 — 8 April, Evening Shift — Question 46

$L_{1}=\frac{x+2}{1}=\frac{y-1}{1}=\frac{z}{1}=\lambda$, any point on it $(\lambda-2, \lambda$ $+1, \lambda)$

$L_{2}=\frac{x-3}{5}=\frac{y}{-1}=\frac{z-1}{1}=\mu$, any point on it $(5 \mu+3$, $-\mu, \mu+1)$

$L_{3}=\frac{x}{-3}=\frac{y-3}{3}=\frac{z-2}{1}=k$, any point on it ( $-3 k$, $3 k+3, k+2)$

$P \equiv$ point of intersection of $L_{1}$ and $L_{2}=(-2,1,0)$

$\mathrm{Q}=$ point of intersection of $L_{1}$ and $L_{3}=(0,3,2)$

$R \equiv$ point of intersection of $L_{2}$ and $L_{3}=(3,0,1)$

$\overline{P Q}=2 \hat{i}+2 \hat{j}+2 \hat{k}$

$\overline{P R}=5 \hat{i}-\hat{j}+\hat{k}$

$A=\frac{1}{2}|\overline{P Q} \times \overline{P R}|=\sqrt{56}$

$A^{2}=56$