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Question

Let a,b and c be three non zero vectors which are pairwise noncollinear. If a+3b is collinear with c and b+2c is collinear with a, then a+3b+6c is:

A
a+c
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B
a
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C
c
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D
0
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Solution

The correct option is D 0
As a+3b is collinear with c;
a+3b=λc(i)
As b+2c is collinear with a;
b+2c=μa(ii)
From (i) we have a+3b+6c=(λ+6)c(iii)
and from (ii) we have a+3b+6c=(1+3μ)a(iv)
Since a is non collinear with c we have λ+6=1+3μ=0
hence from (iii) or (iv) we have a+3b+6c=0

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