# why to calculate unit vectors before calculating their dot product?

• Mar 2nd 2011, 08:17 PM
why to calculate unit vectors before calculating their dot product?
why to calculate unit vectors before calculating their dot product?

Could someone explain this to me?
• Mar 2nd 2011, 08:32 PM
dwsmith
Quote:

Could someone explain this to me?

What?

I don't understand what you are trying to do.

Can you post the exact question you are working on?
• Mar 2nd 2011, 09:20 PM
Lets assume I have many vectors with different lengths and I would like to calculate their angle etc. To do that I need dot product ... but since they have different length is suggested to normalize them (unit vector them) and later take the dot product... so my question is why we need to "unit vector them" first etc. THANKS
• Mar 3rd 2011, 02:18 AM
mr fantastic
Quote:

Lets assume I have many vectors with different lengths and I would like to calculate their angle etc. To do that I need dot product ... but since they have different length is suggested to normalize them (unit vector them) and later take the dot product... so my question is why we need to "unit vector them" first etc. THANKS

Still makes no sense. Post a specific and concrete question.
• Mar 3rd 2011, 02:41 AM
Ackbeet
Quote:

$\displaystyle \mathbf{a}\cdot\mathbf{b}=\|\mathbf{a}\|\,\|\mathb f{b}\|\cos(\theta),$ or
$\displaystyle \cos(\theta)=\dfrac{\mathbf{a}\cdot\mathbf{b}}{\|\ mathbf{a}\|\,\|\mathbf{b}\|},$
where $\displaystyle \theta$ is the angle between them. If $\displaystyle \mathbf{a},\mathbf{b}$ are unit vectors (you've normalized them), then the formula reduces down to
$\displaystyle \mathbf{a}\cdot\mathbf{b}=\cos(\theta).$