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Let veca, vecb and vecc be three non-zer...

Let `veca, vecb and vecc` be three non-zero vectors such that no two of these are collinear.If the vector `veca + 2 vecb` is collinear with `vecc and vecb +3 vecc` is collinear with `veca (lamda` being some non-zero scalar), then` veca + 2 vecb + 6 vecc` equals:

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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