Let a,b and c be three non-zero vectors which are pairwise non-collinear. If a+3b is collinear with c and b+2c is collinear with a, then a+3b+6c is

Options

A. `a+c`
B. a
C. c
D. `vec0`

Answer

D

Explanation

Given, `a + 3` b is collinear with c.
`rArr a + 3b = lambda c "….."(i)`
Also, `b + 3c` is collinear with a.
`rArr b + 2c = mua "…"(ii)`
From Eq. (i) we get
`a + 3b + 6c = (lambda + 6) c "….."(ii)`
From Eq. (ii), we get
`a + 3b + 6 c= (1+3 mu) a"....."(iv)`
On solving Eqs. (iii) and (iv) , we get
`(lambda + 6) c = (1+3 mu) a`
Since, a is not collinear with c.
`rArr lambda + 6 = 1 + 3 mu = 0`
From Eq. (v), we get
`a + 3b + 6 c = 0`