JEE Main 2017 (Offline)Question 1
Given $\vec a=2\hat i+\hat j-2\hat k$ and $\vec b=\hat i+\hat j$. Let $\vec c$ be a vector such that $|\vec c-\vec a|=3$, $|(\vec a\times\vec b)\times\vec c|=3$ and the angle between $\vec c$ and $\vec a\times\vec b$ be $30^\circ$. Then $\vec a\cdot\vec c$ is equal to :
Vector Algebra
Solution
$|\vec a\times\vec b|=|2\hat i-2\hat j+\hat k|=3$; $3|\vec c|\sin30^\circ=3\Rightarrow|\vec c|=2$. From $|\vec c-\vec a|^2=4-2\vec a\cdot\vec c+9=9$, $\vec a\cdot\vec c=2$.