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Let a, b, c be three non-zero vectors, no two of which are collinear. If a + 3b is parallel to c and b + 2c is parallel to a, then the vector a + 3b + 6c is:

1. a
2. c
3. 0
4. a + c

Correct answer: 0

Solution

The conditions given imply that the vectors can be expressed in terms of each other, leading to a situation where the combination of these vectors results in the zero vector. Specifically, since both expressions are parallel to different vectors, their linear combinations ultimately cancel each other out, resulting in the vector being zero.

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