JEE Main 2020 (Online) 5th September Evening ShiftQuestion 1
Let the vectors $\vec{a},\vec{b},\vec{c}$ be such that $|\vec{a}|=2$, $|\vec{b}|=4$ and $|\vec{c}|=4$. If the projection of $\vec{b}$ on $\vec{a}$ is equal to the projection of $\vec{c}$ on $\vec{a}$ and $\vec{b}$ is perpendicular to $\vec{c}$, then the value of $\left|\vec{a}+\vec{b}-\vec{c}\right|$ is $\_\_\_\_\_\_\_\_$ .
Vector Algebra
Answer$6$
Solution
Equal projections on $\vec a$ give $\vec a\cdot\vec b=\vec a\cdot\vec c$, and $\vec b\cdot\vec c=0$. So $|\vec a+\vec b-\vec c|^2=4+16+16+2\vec a\cdot\vec b-2\vec a\cdot\vec c-2\vec b\cdot\vec c=36$, giving $6$.