JEE Main 2020 (Online) 7th January Evening ShiftQuestion 1
Let $\vec a,\vec b$ and $\vec c$ be three unit vectors such that $\vec a+\vec b+\vec c=\vec 0$. If $\lambda=\vec a\cdot\vec b+\vec b\cdot\vec c+\vec c\cdot\vec a$ and $\vec d=\vec a\times\vec b+\vec b\times\vec c+\vec c\times\vec a$, then the ordered pair $(\lambda,\vec d)$ is equal to :
Vector Algebra
Solution
$0=|\vec a+\vec b+\vec c|^2=3+2\lambda\Rightarrow\lambda=-\frac32$. With $\vec c=-\vec a-\vec b$: $\vec b\times\vec c=\vec a\times\vec b$, $\vec c\times\vec a=\vec a\times\vec b$, so $\vec d=3\vec a\times\vec b$.