# Linear algebra

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 :)

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Do you know the definition of the dot product?

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?

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

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

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

Mark44
Mentor
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

This is so vague as to be meaningless.
sorry champ

Mark44
Mentor
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