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Let a, b and c be three non-zero vectors such that no two of these are collinear. If the vector a + 2b is collinear with c and b + 3c is collinear with λ (λ being some non-zero scalar) then a + 2b + 6c equals

1. 0
2. λb
3. λc
4. λa

Correct answer: 0

Solution

Since a+2b is parallel to c, a+2b+6c=(a+2b)+6c is a multiple of c. Since b+3c is parallel to a, a+2b+6c=a+2(b+3c) is a multiple of a. As a and c are non-collinear, the common vector must be 0, so a+2b+6c=0.

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