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1. - 1.71. Our proof of the Cauchy-Schwarz inequality, Theorem 1.13, used that when  $U$ is a unit vector,  $0 \leq ||V−(U·V)U||^2 = ||V||^2 ||V||2  −(U·V)^2$. Therefore if $U$ is a unit vector and equality holds, then $V = (U · V)U$. Show that equality occurs in the Cauchy Schwarz inequality for two arbitrary vectors $V$ and $W$ only if one of the vectors is a multiple (perhaps zero) of the other vector.  Answer: