Chapter 6.2, Problem 2PP

Let y and L be as in Example 3 and Figure 3. Compute the orthogonal projection ŷ of y onto L using u = $\left[\begin{array}{c}2\\ 1\end{array}\right]$ instead of the u in Example 3.

EXAMPLE 3 Let y = $\left[\begin{array}{c}7\\ 6\end{array}\right]$ and u = $\left[\begin{array}{c}4\\ 2\end{array}\right]$. Find the orthogonal projection of y onto u. Then write y as the sum of two orthogonal vectors, one in Span {u} and one orthogonal to u.

FIGURE 3 The orthogonal projection of y onto a line L through the origin.