1.

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+6cis

Answer»

`a+c`
a
c
`vec0`

Solution :Given, `a + 3` b is collinearwith c.
`rArr a + 3B= LAMBDA c "….."(i)`
Also, `b + 3c`is collinearwith 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 solvingEqs. (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`


Discussion

No Comment Found

Related InterviewSolutions