IIT JEE , AIEEE Forum - Mathematics , Algebra

sboosy

I think third part ..what is asked to prove is wrong ...
I think it should have been a+2b+4c = 0

Now since a+2b is collinear with c we have
a+2b = kc ...where k is some constant

Since b+2c is collinear with a we have
b+2c = k'a
=> 2b+4c = 2k'(a)

Subtracting the 2 eqns..we get

a-4c = kc - 2k'a
=> (1+2k')a = (k+4)c .....(1)

Now since a,b,c are such that no 2 are collinear ....
a cannot b expressed solely in terms of c
that is a not equal to lambda c

Thus (1) can have solution only if 1+2k'=0 ..that is k' = -1/2
and k+4 = 0 ..that is k = -4

Substituting this value of k in the very first equation we get

a+2b+4c = 0

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