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Question

If a,b,c are three non-zero vectors, no two of which are collinear, a+b is collinear with c and b+3c is collinear with a, then |a+2b+6c| will be equal to


A

zero

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B

1

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C

9

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D

4

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Solution

The correct option is A

zero


a+2b=λc...(i)b+3c=μa,......(ii)
where no two of a, b and c are collinear vectors
Eliminating b from above relations,
a6c=λc2μaa(1+2μ)=(λ+6)c
Since a, b are non-collinear and non-zero,
1+2μ=0, λ+6=0μ=12, λ=6

a+2b=6ca+2b+6c=0


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