JEE Main 2017 (Online) 9th AprilQuestion 1
If the vector $\vec b=3\hat j+4\hat k$ is written as the sum of a vector $\vec b_1$, parallel to $\vec a=\hat i+\hat j$ and a vector $\vec b_2$, perpendicular to $\vec a$, then $\vec b_1\times\vec b_2$ is equal to :
Vector Algebra
Solution
$\vec b_1=\frac{\vec a\cdot\vec b}{|\vec a|^2}\vec a=\frac32(\hat i+\hat j)$, $\vec b_2=-\frac32\hat i+\frac32\hat j+4\hat k$; $\vec b_1\times\vec b_2=\frac32(4,-4,3)=6\hat i-6\hat j+\frac92\hat k$.