Question

For any two numbers a and b, the product of a−b times itself is equal to a2−2ab+b2.
Does this familiar algebraic result hold for dot products of a vector u − v with itself? In other words, is it true that
(u − v) • (u − v) = u•u−2u•v+v•v? Justify your conclusion,
trying not to express vectors u and v in component form.

Answer 1

Use the property

a dot (b+c) = a dot b + a dot c

Answer 2

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Answer 3

Yes, because of the dot product