AIEEE 2004 (Offline)Question 1
Let $\vec u,\vec v,\vec w$ be such that $|\vec u|=1$, $|\vec v|=2$, $|\vec w|=3$. If the projection of $\vec v$ along $\vec u$ is equal to that of $\vec w$ along $\vec u$ and $\vec v,\vec w$ are perpendicular to each other then $|\vec u-\vec v+\vec w|$ equals :
Vector Algebra
Solution
With $\vec u\cdot\vec v=\vec u\cdot\vec w$ and $\vec v\cdot\vec w=0$: $|\vec u-\vec v+\vec w|^2=1+4+9-2\vec u\cdot\vec v+2\vec u\cdot\vec w-2\vec v\cdot\vec w=14$.