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# ExTrA hArD ChALLeNge iNvoLvinG dOt ProDUcTS

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Let "a" and "b" be two vectors such that neither of a-b and a+b is the zero vector.

(a) Prove that if the vectors a and b are of equal length, then a-b and a+b are perpendicular.

(b) Prove that if a-b and a+b are perpendicular, then a and b are of equal magnitude.

Your solution should not depend on coordinates, slopes, or the properties of geometric figures; try to use vectors! By the way, note that these are the two separate parts of the statement " and  are of equal length if and only if the vectors  and  are perpendicular."

If I could get an explanation over just an answer it would be greatly appreciated

Jun 25, 2021

#1
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Sounds to me like your teacher really wants you to think hard and do some research on your own.

Jun 25, 2021
#2
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I just really want the answer!  I need it soon!

Guest Jun 25, 2021
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Understanding takes time.

When you research and work it out for yourself the understanding will usually be deeper.

Of course, if you just want the answer, that is called cheating.

Melody  Jun 25, 2021
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Pleas help, I really need an answer soon!

Jun 25, 2021