Given vectors a = 3i + 2j + 3k and b = 2i - 3j - 3k, the vector (a x b) x (a + b) is collinear with which of the following vectors?

4i + j + 4k
i + 5j + 6k
5i + 4j + 5k
5i + 5k

Correct answer: i + 5j + 6k

Solution

Computing a x b = (3i+2j+3k) x (2i-3j-3k) = 3i + 15j - 13k. Then (a x b) x (a+b) = (3i+15j-13k) x (5i-j+0k) = -13i - 65j - 78k = -13(i + 5j + 6k), which is a scalar multiple of i + 5j + 6k.

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