Let a, b and c be 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 (`lambda` being some non-zero scalar), then `a+2b+6c` equals to

Options

A. `lambdaa`
B. `lambdab`
C. `lambdac`
D. 0

Answer

D

Explanation

If `a + 2b` is collinear with c, then
`a + 2b = tc "…"(i)`
Also, `b+3c` is collinear with a, then
`b + 3c = lambda`
`rArr b= lambda a - 3c "…."(iii)`
From Eqs. (i) and (ii), we get
`a + 2(lambdaa - 3c) = t c`
`rArr (a-6c) = t c - 2lambda a`
On comparing the coefficients of a and b, we get
`1= -2lambda`
`rArr lambda = - 1/2 ` and `- 6 = t`
`rArr t = - 6`
`rArrt = - 6`
From Eq. (i) we get
`a + 2b = -6c`
`rArr a + 2b+6c = 0`