JEE Main 2026 (Online) 6th April Evening ShiftQuestion 1
Let $\vec{a}=2\hat{i}+3\hat{j}+3\hat{k}$ and $\vec{b}=6\hat{i}+3\hat{j}+3\hat{k}$. Then the square of the area of the triangle with adjacent sides determined by the vectors $\left(2\vec{a}+3\vec{b}\right)$ and $\left(\vec{a}-\vec{b}\right)$ is :
Vector Algebra
Solution
$\vec u=2\vec a+3\vec b=(22,15,15)$ and $\vec v=\vec a-\vec b=(-4,0,0)$. $\vec u\times\vec v=(0,\,-60,\,60)$, with $|\vec u\times\vec v|^2=7200$. Area $=\frac12|\vec u\times\vec v|$, so (area)$^2=\frac{7200}{4}=1800$. Option (C).