Question

Prove that the two vectors a and b are perpendicular if and only if |a+b|² = |a|² + |b|².

Answer 1

If a and b are perpendicular,

a•b=0

Hence,

(a+b)(a+b)=|a+b|²= |a|²+|b|²+2a•b

=|a|²+|b|²+0=|a|²+|b|²

Thus, proved.

For the converse, reverse the steps.