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

Let `veca, vecb` and `vecc` be three non-zero vectors which are positive non-collinear. If `veca + 3vecb`is collinear with `vecc`and `vecb + 2vecc` is collinear with `veca` then `veca` then `veca + 3vecb + 6vecc` is:

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Given `veca + 2 vecb =lamda vecc" " ` (i)
and `" " vec b + 3 vecc = mu veca, " "` (ii) ltBrgt where two of `veca, vecb and vecc` are collinear vectors.
Eliminating `vecb` from the above relations, we have
`" " veca - 6 vecc = lamda vecc - 2 mu veca`
`" " veca (1+2mu) = (lamda +6) vecc`
`rArr " " mu = -(1)/(2) and lamda -6` as `veca and vecc` are non-collinear.
Putting `mu = -(1)/(2) `in (ii) `or lamda =-6` in (i), we get
`" " veca + 2 vecb + 3vecc = vec0`
or `" " |veca + 2vecb + 3vecc|=0`
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