Let vector a = i + 2j - 3k and vector b = 2i + j - k. Vector u satisfies both a cross u = a cross b and a dot u = 0. Find the value of 2|u|².

Correct answer: 5

Solution

a cross (u - b) = 0 means u - b = lambda*a. Substituting into a dot u = 0: a dot b + lambda*|a|² = 0, giving lambda = -1/2. Then u = (3/2)i + (1/2)k, |u|² = 5/2, so 2|u|² = 5.

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