# Thread: 3 vectors has same magnitude

1. ## 3 vectors has same magnitude

hi
I've tried to solve a problem which is saying that I've A,B and C are 3 vectors in R^3 and has a magnitude of 2 such that a+b+c=0 find the value of (a.b)+(b.c)+(a.c)

first, A+B= -c

so (A+B).C= 2 * 2* cos 180 = -4

So A.C + B.C= -4

and I've do so for A+c=-b

so i got (A.b)+(b.c)= -4

and I found that (A.B)= (A.C) i.e the angle between A and B is the same as the angle btwen A and C

Anyway I can't go on from here. If that's right how can i get the last result . and if not .. please, tell me what is wrong

2. ## Re: 3 vectors has same magnitude

Originally Posted by ahmedzoro10
hi
I've tried to solve a problem which is saying that I've A,B and C are 3 vectors in R^3 and has a magnitude of 2 such that a+b+c=0 find the value of (a.b)+(b.c)+(a.c)
HINT:
$C\cdot C=4$ so $A\cdot C+B\cdot C+4=0$

Do that twice more using $B~\&~A.$ Then add.

3. ## Re: 3 vectors has same magnitude

Originally Posted by Plato
HINT:
$C\cdot C=4$ so $A\cdot C+B\cdot C+4=0$

Do that twice more using $B~\&~A.$ Then add.
Still unreachable , sorry

4. ## Re: 3 vectors has same magnitude

I've got that

A.c + B.c+C.c=0
A.b+b.c+b.b=0
a.b+A.c+a.a=0

5. ## Re: 3 vectors has same magnitude

Originally Posted by ahmedzoro10
Still unreachable , sorry
I am not going to complete the problem for you.
This is the last hint I will give.
$\begin{array}{l} A \cdot C + B \cdot C = - 4 \\ A \cdot B + B \cdot C = - 4 \\ A \cdot B + A \cdot C = - 4 \\ \end{array}$

You want $A \cdot B + B \cdot C + A \cdot C = ?$

6. ## Re: 3 vectors has same magnitude

OMG!! I've reached this equations 2 hrs ago but I was like a drunk.

Thanks alot