Question

Suppose that u and v are unit vectors. The angle between which is pi/4. Let a = u+3sqrt(2)v. By considering a dot a find |a|

Answer 1

http://i987.photobucket.com/albums/ae358/mgeorgiou18/answer.png

Answer 2

I don't understand the answer. Can anyone explain?

Answer 3

They just went through and distributed the dot product if you have:
\[(\vec{u}+\vec{v})\cdot(\vec{u}+\vec{v})=\vec{u} \cdot \vec{u}+\vec{u} \cdot \vec{v}+\vec{v} \cdot \vec{u}+\vec{v} \cdot \vec{v}\]
Which is what they did, then you know that they are unit vectors so u dot u =1 (the magnitude) then the just combined to get 25 (since the dot product gives you a scalar) then took the square root to get |a|

Answer 4

but where does the "1*1*(1/sqrt(2))" come from?

Answer 5

doesn't (u dot v) = 0?

Answer 6

U dot V is only zero if the vectors are orthogonal. But since that is not specified then you cannot assume it.

Answer 7

And the 1/sqrt(2) comes from where they factored out the 3sqrt(2) but v doesn't have it so you have to have 1/sqrt(2) to compensate.

Answer 8

Thanks, I understand now :)

Answer 9

You're welcome :D