but I'm not sure if that's right.
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Do you mean this problem?
You might take a look at Problem 45 on page 565 of the textbook, which validates your approach if you're willing to believe the result of the problem without actually doing it. Or, for P=(1,1,1), Q=(2,1,3), R=(4,2,3), you could compute it as we've discussed extensively in class (for example see the lecture notes for 8/31/18) as
||PR - (PR∙PQ)/(PQ∙PQ) PQ||
