a,b,c are three non zero vectors no two of which are collinear If the collinear .If the vectors a+2b is the collinear with c and b+3c is collinear with a,a+2b+6c is equal to

Dear pallavi

let a+2 b = u c  ............1

and   b+3c =va ............2

put replace vctor a from 1 and b

 b+3c =v(uc-2b)

or  (1+2v)b=(uv-3)c

since b and c are not colinier so

 1+2v =0   or v=-1/2

and uv-3=0   or u=-6

put value of u in equation 1

a+2b=-6c

a+2b+6c=0

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Badiuddin

Let a+2b=kc b+3c=qa From the first equation, we get, b=(kc-a)/2 Substituting in the other equation, we get (k+6)c=(2q+1)a But as these vectors are not collinear, so the L.H.S. and R.H.S. must be equal to zero independently. So we get (k+6)=0 k=-6 So a+2b= -6c a+2b+6c=0