# Math Help - Dot Product problem!!!

1. ## Dot Product problem!!!

Hi all,

I have 3 pairs of 3-dimensional unit vectors. I take the dot product of those pairs of vectors and so I obtain the angle between them. In other words I can express the three dot products by their respective angle $\cos\theta_1$, $\cos\theta_2$ and $\cos\theta_3$. I was wondering if there is any interesting geometric interpretation by the addition of those three angles $\cos\theta_1$ + $\cos\theta_2$ + $\cos\theta_3$?

I am trying to find a way of simplifying/re-writing the above addition of angles and hence express it as a single term.

I would appreciate anyones help

Regards

Alex

2. Originally Posted by tecne
Hi all,

I have 3 pairs of 3-dimensional unit vectors. I take the dot product of those pairs of vectors and so I obtain the angle between them. In other words I can express the three dot products by their respective angle $\cos\theta_1$, $\cos\theta_2$ and $\cos\theta_3$. I was wondering if there is any interesting geometric interpretation by the addition of those three angles $\cos\theta_1$ + $\cos\theta_2$ + $\cos\theta_3$?

I am trying to find a way of simplifying/re-writing the above addition of angles and hence express it as a single term.

I would appreciate anyones help

Regards

Alex
I don't know about the sums of the cosines, but in general
$cos^2(\theta _1) + cos^2(\theta _2) + cos^2(\theta _2) = 1$

-Dan