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we have vectors u and v whose magnitude and the angle between them are given and this is about whether you know the basic definition of the dot products and the cross products so first the dot product of course you probably remember that product as component wise multiplication and then you add them but what if the components are not given how do you find the dot product weamp;#39;ll use the original definition of the dot product which is you take the norm of the first norm of the second and multiply by the cosine of the angle between so ing to that if you have a u dot v it would be norm of the first one which is 2 norm of the second one which is six those are given here right and the angle between them is 30 degrees and 30 degrees is cosine 30 degrees is square root of three over two and i guess 2 2 cancels and the answer is 6 radical 3. now what about v dot v then well in this case you have v v and the angle between v and v would be zero degrees right so you end up with v is six the
