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In the second case, when $W$ is nonzero, then consider the unit vector $U = \frac{W}{||W||}$. Then, by the result in the question, it follows that $V = (U · V)U$. Therefore:  $$V = (U · V)U = (\frac{W}{||W||}· V)·\frac{W}{||W||}= (\frac{W·V}{W^2})·W$$  As $(\frac{W·V}{W^2})$ is a constant, so $V $V$  is a multiple of W$. $W$.