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Let veca, vecb, vecc be three non-zero v...

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

A

a+c

B

a

C

`c`

D

0

Text Solution

Verified by Experts

The correct Answer is:
D
As, a+3b is collinear with c.
`thereforea+3b=lamdac` . . . (i)
Also, b+2c is collinear with a.
`implies b+2c=mua` . . (ii)
From eq. (ii), we get
`a+3b+6c=(lamda+6)c` . .. (iii)
From eq. (ii), we get
`a+3b+6c=(1+3mu)a` . . (iv)
From eqs. (iii) and (iv), we get
`therefore(lamda+6)c=(1+3mu)a`
Since, a is not collinear with c.
`implies lamda+6=1+3mu=0`
from eq. (iv), we get
`a+3b+6c=0`.
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