In Figure 9.3.8, you can see illustrations of splitting \(\vu\) into two parts: \(\vw_1\text{,}\) which is parallel to \(\vv\text{,}\) and \(\vw_2\text{,}\) which is orthogonal to \(\vv\text{.}\) Use this figure for reference as you do the following.
We know from the previous subsection that there is a third configuration of vectors, which occurs when \(\vu\) and \(\vv\) are orthogonal. Suppose that \(\vu\) and \(\vv\) are nonzero orthogonal vectors. What would \(\vw_1\) and \(\vw_2\) be in this case?
We want to switch the roles of \(\vu\) and \(\vv\) for the examples in the previous parts. Specifically, for these configuration of vectors, we want to split \(\vv\) into parts that are parallel to \(\vu\text{,}\) which we will call \(\vz_1\text{,}\) and orthogonal to \(\vu\text{,}\) which we will call \(\vz_2\text{.}\) On Figure 9.3.9, draw \(\vz_1\) and \(\vz_2\) for each configuration.
