Let a, b, c be three vectors such that every pair is non-collinear. The vector (a + 3b) is collinear with c, and the vector (2b + 3c) is collinear with a. If |b| = 1, find the value of |2a + 3b + 9c|.

Correct answer: 3

Solution

Solving the system gives lambda = -9/2 and mu = -2/3. Then a = (-9/2)c - 3b, so 2a = -9c - 6b, and 2a + 3b + 9c = -6b - 9c + 3b + 9c = -3b. Hence |2a + 3b + 9c| = 3|b| = 3*1 = 3.

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