Use the property
a dot (b+c) = a dot b + a dot c
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.
3 answers
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Yes, because of the dot product