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Question: guided proof prove that if u is orthogonal to...

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Guided Proof :

Prove that if u is orthogonal to v and w, then u is orthogonal to cv + dw for any scalars c and d.

Getting Started: To prove that u is orthogonal to cv + dw, you need to show that the dot product of u and cv + dw is 0.

(i) Rewrite the dot product of u and cv + dw as a linear combination of (u _ v) and (u _ w) using Properties 2 and 3 of Theorem 5.3.

(ii) Use the fact that u is orthogonal to v and w, and the result of part (i), to lead to the conclusion that u is orthogonal to cv + dw.

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