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Let's consider the following cross product
(A + B) X (A - B)
if the two ar mutually perpendicular then Cosα (where α is the angle between them) would be zero
so,
(A + B) X (A - B) = 0
thus
(A X A) - (B X B) - (A X B) + (B X A) = 0
or
A2 - B2 = 0 ( A X B = - B X A )
thus, we get
A = B
so the two vectors are equal in magnitude
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