JEE Main 2022 (Online) 27th July Morning ShiftQuestion 1
Let $\vec a=\alpha\hat i+\hat j+\beta\hat k$ and $\vec b=3\hat i-5\hat j+4\hat k$ be two vectors, such that $\vec a\times\vec b=-\hat i+9\hat i+12\hat k$. Then the projection of $\vec b-2\vec a$ on $\vec b+\vec a$ is equal to
Vector Algebra
Solution
(Reading the printed $9\hat i$ as $9\hat j$.) $\vec a\times\vec b=(4+5\beta,\ 3\beta-4\alpha,\ -5\alpha-3)=(-1,9,12)$. $\beta=-1$, $\alpha=-3$ (check: $3\beta-4\alpha=9$). So $\vec a=(-3,1,-1)$. $\vec b-2\vec a=(9,-7,6)$, $\vec b+\vec a=(0,-4,3)$, $|\vec b+\vec a|=5$. Projection $=\frac{0+28+18}{5}=\frac{46}5$. Option (D).