4. Suppose \ vec v_{1} , vec v 2 ,..., vec v k \ is an orthogonal set. Prove, using math- ematical induction, that || vec v_{1} + vec v 2 +*+ vec v k ||^ 2 =|| vec v 1 ||^ 2 +|| vec v 2 ||^ 2 +*+|| vec v k ||^ 2 . [6]
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