Let V = (0,3,2) and A = (-1,0,1). Let P be the point on the line passing through A with direction vector (1,1,1) that is closest to

Hint: If you project the vector $\overrightarrow{AV}$ onto the line, take the projection as $\overrightarrow{p}$, $\overrightarrow{p}$ is actually $\overrightarrow{OP} - \overrightarrow{OA}$.