Def1: dot product is the sum of corresponding cartesian co-ordinates.

Def2: dot product is the product of two vector lenths, and the cosine of their angle.

Usually this is proved within a triangle consisting of vector OA, OB, and AB=OB-OA

In a catesian system, distance formula is true based on Pythagoras' Theorem.

So if you define A(x[sub]1[/sub],y[sub]1[/sub],z[sub]1[/sub]) B(x[sub]2[/sub] ,y[sub]2[/sub],z[sub]2[/sub]), you get

meanwhile, Cosine Theorem

then below must be valid

proven

]]>u.v = |u|*|v|

And thus, a = |u| / |v| so:

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If the normal of u cross v is 0, then u dot v equals a times the normal of v squared.

Is that right?

]]>I know that both u and v are parallel vectors and that norm(u X v) sin x = 0

Then I got stuck.

Anyone knows any good resources for me to learn linear algebra (preferably from the basics, with exercises and answers)? I'm finding it v hard to understand this topic.

Thanks.

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