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Question

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 a(λ being some non-zero scalar), then a+2b+6c equals

A
λa
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B
λb
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C
λc
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D
0
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Solution

The correct option is C 0
a+2b=λc(i)
b+3c=μa(ii)
Substitutingafrom(i)in(ii)
b+3c=μ(λc2b)
(1+2μ)b=(λμ3)c
Butsincebandcarenotcollinear.
Either1+2μ=0,λμ3=0
μ=12
andλ2=3
λ=6

Substitutingin(i)
a+2b+6c=0

D)Answer.


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