Let R4 have the Euclidean inner product. (a) Find a vector in R4 that is orthogonal to

Chapter 6, Problem 1

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Let R4 have the Euclidean inner product. (a) Find a vector in R4 that is orthogonal to u1 = (1, 0, 0, 0) and u4 = (0, 0, 0, 1) and makes equal angles with u2 = (0, 1, 0, 0) and u3 = (0, 0, 1, 0). (b) Find a vector x = (x1, x2, x3, x4) of length 1 that is orthogonal to u1 and u4 above and such that the cosine of the angle between x and u2 is twice the cosine of the angle between x and u3.

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