Proving Parallel Vectors: |u•v| = ||u|| ||v||

[dangish]

Question: Show that |u dot v| = ||u|| ||v|| if and only if u and v are parallel.

I know that u and v are parellel if their dot product is 1.

so if |u dot v| = 1 , fair enough, but how can I show that ||u|| ||v|| will also be equal to 1

any help would be greatly appreciated, thanks in advance :)

 

[sponsoredwalk]

Do you know the definition of the dot product?

 

[micromass]

I know that u and v are parellel if their dot product is 1.

This is not true. You must have misunderstood something...

How did you define the dot product?

 

[dangish]

Not really.. it's just the product of two vectors isn't it?

 

[sponsoredwalk]

No, check out the proper definition and then look at your problem again, it should become very clear

 

[dangish]

Could you perhaps tell me your definiton of the dot product? :D

 

[Mark44]

Not really.. it's just the product of two vectors isn't it?

This is so vague as to be meaningless.

Could you perhaps tell me your definiton of the dot product? :D

You tell us, please.

 

[sponsoredwalk]

Ah I'm sorry, it's not really straight from the definition you can prove this, it comes from
a theorem. I'm just so used to seeing it called a definition.

Read this page:

http://tutorial.math.lamar.edu/Classes/CalcII/DotProduct.aspx

and you should be able to answer this question.

 

[dangish]

This is so vague as to be meaningless.

sorry champ

 

[Mark44]

My point is that since there are several ways that vectors can be multiplied, you need to be more specific.

u \cdot v - the dot product, sometimes called the scalar product because it results in a scalare
u X v - the cross product for vectors in R³
av - scalar multiplication of a scalar and a vector