Given vectors prove that

if and only if and are orthogonal.

*Proof.*

From Theorem 13.12(f) (page 483 of Apostol) we know

But if and only if and are orthogonal (from the definition of orthogonality). Thus, if and only if and are orthogonal

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Stumbling Robot

A Fraction of a Dot
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Prove that the norm of the cross product is the product of the norms if and only if *A* and *B* are orthogonal

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### Point out an error, ask a question, offer an alternative solution (to use Latex type [latexpage] at the top of your comment):

Given vectors prove that

if and only if and are orthogonal.

*Proof.*

From Theorem 13.12(f) (page 483 of Apostol) we know

But if and only if and are orthogonal (from the definition of orthogonality). Thus, if and only if and are orthogonal

There is a typo in the formula as stated. Instead of adding the squared norms of A and B, you need to multiply them instead