• 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 $\vec u \cdot \vec v=|u||v| \cos\theta$

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

For $\vec u = $

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

We can also find the dot product which is,

$\vec u = \\\ \vec v = $

$\vec u \cdot \vec v = \cdot = ax+by+cz$

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