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

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- Nov 11th 2010, 07:39 AMMcooltaVectors 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, 07:46 AMAckbeet
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, 08:07 AMPlato
- Nov 11th 2010, 08:13 AMMcoolta
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, 08:24 AMPlato
Before, you left out a most important word: UNIT.

Because they are units, recall that $\displaystyle \left\| A \right\|=1$

$\displaystyle \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, 08:43 AMMcoolta
Ah ok, thanks. So i get a.b + b.c + c.a = -3/2 ?

- Nov 13th 2010, 11:40 AMHallsofIvy
Yes.