Proof: Calculus and vectors

Prove that a parallelogram is a rectangle of and only if its diagonals are equal in length.

This is in a calculus course, and we are going over vectors. SO please only proofs having to do with vectors please. Thank you.

let < a > and < b > be the side vectors..| d1 | = { | a |² + | b | ² - 2 ' a dot b ' cos Θ1 }^(1/2)

and | d2 | = { | a |² + | b |² - 2 ' a dot b ' cos Θ2 }^(1/2)

thus | d1 | = | d2 | iff cos Θ1 = cos Θ2 & Θ1 + Θ2 = π

OR : d1 = a + b ---> d1 'dot' d1 = a'dot'a + 2 a'dot'b + b'dot'b

and d2= a - b ---> d1 'dot ' d2 = a ' dot ' a - 2 a 'dot ' b + b 'dot ' b

since the left sides are equal iff a ' dot ' b = 0 then a must be orthogonal to b