• May 27th 2008, 03:59 PM
jdt214
Hey guys.. new here.. my precalc hw due 2morro.. with dot products and stuff

Find the Angle theta between the vectors

19: u = <2i-j> v = -2j

21: u = <5i+5j> v=<-6i +6i>

23: u=cos(pi/3)i + sin(pi/3)j v = cos(3pi/4)i + sin(3pi/4)j

• May 27th 2008, 06:29 PM
Jen
Quote:

Originally Posted by jdt214
Hey guys.. new here.. my precalc hw due 2morro.. with dot products and stuff

Find the Angle theta between the vectors

19: u = <2i-j> v = -2j

21: u = <5i+5j> v=<-6i +6i>

23: u=cos(pi/3)i + sin(pi/3)j v = cos(3pi/4)i + sin(3pi/4)j

The dot product is defined as $\displaystyle \vec u \cdot \vec v=|u||v| \cos\theta$

In each of these problems you are given two vectors, we can find the magnitude of each by using this formula,

For $\displaystyle \vec u = <a,b,c>$

$\displaystyle |u|=\sqrt{a^2+b^2+c^2}$

We can also find the dot product which is,

$\displaystyle \vec u = <a,b,c> \\\ \vec v = <x,y,z>$

$\displaystyle \vec u \cdot \vec v = <a,b,c> \cdot <x,y,z> = ax+by+cz$

Being able to find the dot product and the magnitude we can plug these values into the original equation $\displaystyle \vec u \cdot \vec v=|u||v| \cos\theta$
and solve for $\displaystyle \theta$