Math Problem Statement
Show that if ||u|| = ||v|| for vectors u and v, then u + v and u − v are orthogonal.
Solution
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Math Problem Analysis
Mathematical Concepts
Vector Algebra
Dot Product
Orthogonality
Formulas
(u + v) · (u - v) = u · u - u · v + v · u - v · v
Theorems
Properties of the Dot Product
Orthogonal Vectors
Suitable Grade Level
Grades 11-12