$$(v-w)\cdot v+v\cdot w= \|v\|^2.$$
Work Step by Step
Using the properties of the dot product, we have $$(v-w)\cdot v+v\cdot w=v\cdot v -w\cdot v+v\cdot w\\ =v\cdot v -v\cdot w+v\cdot w=v\cdot v=\|v\|^2.$$
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