JEE Main 2021 (Online) 16th March Evening ShiftQuestion 1
Let $\vec{c}$ be a vector perpendicular to the vectors $\vec{a}=\hat{i}+\hat{j}-\hat{k}$ and $\vec{b}=\hat{i}+2\hat{j}+\hat{k}$. If $\vec{c}\cdot\left(\hat{i}+\hat{j}+3\hat{k}\right)=8$ then the value of $\vec{c}\cdot(\vec{a}\times\vec{b})$ is equal to $\_\_\_\_\_\_$ .
Vector Algebra
Answer$28$
Solution
$\vec a\times\vec b=(3,-2,1)$ and $\vec c=t(3,-2,1)$. $\vec c\cdot(1,1,3)=t(3-2+3)=4t=8\Rightarrow t=2$. $\vec c\cdot(\vec a\times\vec b)=2|\vec a\times\vec b|^2=2\cdot14=28$.