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if |a+b|=|a-b|, then what is the angle between the vectors a and b?

$Given | \bar{a} + \bar{b} | = | \bar{a} - \bar{b} | squaring on both sides we get | \bar{a} + \bar{b} |^{2} = | \bar{a} - \bar{b} |^{2} \Rightarrow {| \bar{a} |}^{2} + {| \bar{b} |}^{2} + 2 \bar{a} . \bar{b} = {| \bar{a} |}^{2} + {| \bar{b} |}^{2} - 2 \bar{a} . \bar{b} \Rightarrow 4 \bar{a} . \bar{b} = 0 \Rightarrow \bar{a} . \bar{b} = 0 \Rightarrow \bar{| a |} \bar{| b |} \cos θ = 0 \Rightarrow \cos θ = 0 \Rightarrow θ = 90^{0} Angle between the vectors \bar{a} and \bar{b} is 90^{0}$

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