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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

`lamda a`

B

`lamdab`

C

`lamda c`

D

`0`

Text Solution

Verified by Experts

The correct Answer is:
D
If a+2b is collinear with c, then a+2b=tc . . . (i)
also, b+3c is collinear with a, then
`b+3c=lamda a`
`implies b=lamda a-3c` . . (ii)
from eqs. (i) and (ii), we get
`a+2(lamda a-3c)=tc`
`implies (a-6c)=tc-2lamda a`
on comparing the coefficient of a and c, we get
`1=-2lamda implies lamda=-(1)/(3)`
and `-6=t implies t=-6`.
From eq. (i) we get,
`a+2b=-6c` ,brgt `implies a+2b+6c=0`
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