In this problem we show that if u and v are perpendicular vectorsin R2, then u v = 0
Chapter 8, Problem 72(choose chapter or problem)
In this problem we show that if u and v are perpendicular vectorsin R2, then u v = 0. The method of proof is different fromthe one given at the start of the subsection Orthogonal Vectors.(a) Given nonzero vectors u and v orthogonal in R2, show thatu, v, and uv are the lengths of the sides of a right triangle.(b) Use the version of the Pythagorean Theorem you learned inhigh school geometry to show thatu2 + v2 = u v2(c) Write the equation in (b) in terms of dot products and thensimplify to show that u v = 0.
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