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3. a. Consider R^2 with the Euclidean inner product (i.e. dot product). Let v = (x1,...

3. a. Consider R^2 with the Euclidean inner product (i.e. dot product). Let

v = (x1, x2) ? R^2. Show that (x2, ?x1) is orthogonal to v.

b. Find all vectors (x, y, z) ? R^3 that are orthogonal (with the Euclidean

inner product, i.e. dot product) to both (1, 3, ?2) and (2, 7, 5).

C.Let V be an inner product space. Suppose u is orthogonal to both v

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

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