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If a,b and c are three non-zero vectors ...

If a,b and c are 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(`lamda` being some non-zero scalar), then a+2b+6c is equal to

A

A. 0

B

B. `lamdab`

C

C. `lamdac`

D

D. `lamda a`

Text Solution

Verified by Experts

The correct Answer is:
A
As `a+2b` and c are collinear a+2b=`lamdac` . . (i)
Again, b+3c is collinear with a. ltbr. `therefore b+3c=mua` . . . (ii)
Now, `a+2b+6c=(a+2b)+6c=lamdac+6c`
`=(lamda+6)c` . . (iii)
Also, `a+2b+6c=a+2(b+3c)=a+2mua`
`=(2mu+1)a` . . . (iv)
From eqs. (iii) and (iv), we get
`(lamda+6)c=(2mu+1)a`
but a and c are non-zero non-collinear vectors,
`thereforelamda+6=0=2mu+1`
Hence, `a+2b+6c=0`.
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