why to calculate unit vectors before calculating their dot product?

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March 2nd 2011, 08:17 PM
problady

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?
March 2nd 2011, 08:32 PM
dwsmith

Quote:

Originally Posted by problady

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?
March 2nd 2011, 09:20 PM
problady

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
March 3rd 2011, 02:18 AM
mr fantastic

Quote:

Originally Posted by problady

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.
March 3rd 2011, 02:41 AM
Ackbeet

Quote:

Originally Posted by problady

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

I would say you don't. It's six of one, a half-dozen of the other. The formula for dot product is

$\mathbf{a}\cdot\mathbf{b}=\|\mathbf{a}\|\,\|\mathb f{b}\|\cos(\theta),$ or

$\cos(\theta)=\dfrac{\mathbf{a}\cdot\mathbf{b}}{\|\ mathbf{a}\|\,\|\mathbf{b}\|},$

where $\theta$ is the angle between them. If $\mathbf{a},\mathbf{b}$ are unit vectors (you've normalized them), then the formula reduces down to

$\mathbf{a}\cdot\mathbf{b}=\cos(\theta).$

However, you've had to do the work of normalizing. So it's either normalize first and use a slightly simplified dot product formula, or just use the full dot product formula. You'll have to divide by the lengths either way.