JEE Main 2019 (Online) 9th April Morning ShiftQuestion 1
Let $\vec\alpha=3\hat i+\hat j$ and $\vec\beta=2\hat i-\hat j+3\hat k$. If $\vec\beta=\vec\beta_1-\vec\beta_2$, where $\vec\beta_1$ is parallel to $\vec\alpha$ and $\vec\beta_2$ is perpendicular to $\vec\alpha$, then $\vec\beta_1\times\vec\beta_2$ is equal to :
Vector Algebra
Solution
$\vec\beta_1=\frac{\vec\alpha\cdot\vec\beta}{|\vec\alpha|^2}\vec\alpha=\frac12(3,1,0)$, $\vec\beta_2=\vec\beta_1-\vec\beta=(-\frac12,\frac32,-3)$; $\vec\beta_1\times\vec\beta_2=\frac12(-3,9,5)$.