JEE Main 2013 (Online) 23rd AprilQuestion 1
If $\vec a$ and $\vec b$ are non-collinear vectors, then the value of $\alpha$ for which the vectors $\vec u=(\alpha-2)\vec a+\vec b$ and $\vec v=(2+3\alpha)\vec a-3\vec b$ are collinear is :
Vector Algebra
Solution
Collinear: $\vec u=k\vec v$ with $\vec a,\vec b$ independent: $\alpha-2=k(2+3\alpha)$, $1=-3k$. So $k=-\frac13$, $3\alpha-6=-2-3\alpha$, $\alpha=\frac23$.