Vectors' sum :

If |a|=5, |b|=12, |c|=13; and a+b+c = 0, find the value of a.b + b.c + c.a

I'm getting the answer as -169, whereas the answer given is -15. Where am I going wrong?

Question

Vectors' sum : 

If |a|=5, |b|=12, |c|=13; and a+b+c = 0, find the value of a.b + b.c + c.a 


I'm getting the answer as -169, whereas the answer given is -15. Where am I going wrong?

kc_kennylau · Answer

If |a|=5 and |b|=12 and |c|=13 how can a+b+c ever be 0

sumeer · Answer

its vector sum :D

anonymous · Answer

a, b, c are vectors.

kc_kennylau · Answer

oh sorry

anonymous · Answer

It's okay :D

kc_kennylau · Answer

|dw:1386515950056:dw|
I assume this pic is correct?

kc_kennylau · Answer

sorry i'm not quite good in vectors

sumeer · Answer

yea i think so

anonymous · Answer

I'd show you guys how I worked it out .. 

given, a=5, b=12, c=13 ..and a+b+c = 0 
=> (a+b+c)^2=0
=> a^2 + b^2 + c^2 + 2(a.b+b.c+c.a)=0
=> a.b + b.c + c.a = -338/2 = -169

sumeer · Answer

|dw:1386516238353:dw|
i think this is possible too, this may cause the double answer, i hope it its not true it'll lead u an inspiration