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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.

 Jan 26, 2022
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Just consider the scalar product (a + b).(a - b).

That answers both parts.

 Jan 27, 2022

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