Facing problem in a questions on Vectors

If |vector a+vector b|= |vector a- vector b| show that vector a is perpendicular to vector b.

A friend of mine suggested me to square both the sides of the equation. At the end, the result was vector a. vector b=0, from which it could be proved that the vectors are perpendicular. But why do we use the dot product and not the cross product?


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