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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
λ¯¯¯a
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B
λ¯¯b
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C
λ¯¯c
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D
¯¯¯0
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Solution

The correct option is D ¯¯¯0
a+2b is collinear with c.

So we can write:
a+2b=t1c.......(i)
Similarly, b+3c is collinear with a.

So we can write b+3c=t2a.........(ii)
To eliminate b we will perform (i)2(ii) to get
a6c=t1c2t2a

(1+2t2)a(6+t1)c=0
Since a and c are non-collinear, both 1+2t2 and 6+t1 must be zero to satisfy above equation.
t2=12 and t1=6
Substituting the values of t2 and t1 in (i) we get
a+2b+6c=0

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