Science:Math Exam Resources/Courses/MATH152/April 2016/Question A 21/Hint 3

Let $\pi _{1}$ denote the projection onto $L_{1}$ and let $\pi _{2}$ denote the projection onto $L_{2}$. Use the geometric interpretation of projection onto a line to determine the range of $\pi _{1}$. Then, use the same argument, and the fact that $L_{1}$ and $L_{2}$ are perpendicular, to determine the range of $\pi _{2}\circ \pi _{1}$.