# Vectors Question

• Nov 11th 2010, 08:39 AM
Mcoolta
Vectors Question
Ok, so i have Vectors A + B + C = 0

From this, am i right in thinking that it forms an equilateral triangle? Or is that incorrect?

I need to use the above to find the answer to a.b + b.c + c.a
• Nov 11th 2010, 08:46 AM
Ackbeet
The three vectors form a triangle, but you are by no means guaranteed that it is an equilateral triangle. As for your answer, what kind of an answer are you to compute? I don't think you're going to be able to find the exact number.
• Nov 11th 2010, 09:07 AM
Plato
Quote:

Originally Posted by Mcoolta
Ok, so i have Vectors A + B + C = 0
From this, am i right in thinking that it forms an equilateral triangle? Or is that incorrect?
I need to use the above to find the answer to a.b + b.c + c.a

It seems as if you have simply posted only a piece of a problem.
If you post the complete question, we may be able to help you with it.
• Nov 11th 2010, 09:13 AM
Mcoolta
Using three unit vectors a, b, c, so that A+B+C = 0, find a.b + b.c + c.a

Thats all that was given in the question.
• Nov 11th 2010, 09:24 AM
Plato
Before, you left out a most important word: UNIT.
Because they are units, recall that $\left\| A \right\|=1$

$\begin{gathered}
\left( {A + B + C} \right) \cdot \left( {A + B + C} \right) = 0 \hfill \\
\left\| A \right\|^2 + \left\| B \right\|^2 + \left\| C \right\|^2 + 2A \cdot B + 2A \cdot C + 2C \cdot B = 0 \hfill \\
\end{gathered}$
• Nov 11th 2010, 09:43 AM
Mcoolta
Ah ok, thanks. So i get a.b + b.c + c.a = -3/2 ?
• Nov 13th 2010, 12:40 PM
HallsofIvy
Yes.