1.

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

Answer»

`lambdaa`
`LAMBDAB`
`lambdac`
0

Solution :If `a + 2B` is collinearwith c, then
`a + 2b = tc "…"(i)`
Also, `b+3c` is collinearwith 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 comparingthe 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`


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