JEE Main 2020 (Online) 6th September Evening ShiftQuestion 1
If $\vec x$ and $\vec y$ be two non-zero vectors such that $|\vec x+\vec y|=|\vec x|$ and $2\vec x+\lambda\vec y$ is perpendicular to $\vec y$, then the value of $\lambda$ is ________.
Vector Algebra
Answer$1$
Solution
$|\vec x+\vec y|^2=|\vec x|^2\Rightarrow2\vec x\cdot\vec y+|\vec y|^2=0\Rightarrow\vec x\cdot\vec y=-\frac{|\vec y|^2}2$. $(2\vec x+\lambda\vec y)\cdot\vec y=0\Rightarrow-|\vec y|^2+\lambda|\vec y|^2=0\Rightarrow\lambda=1$.