polar equations and vectors problem

• July 28th 2008, 12:03 PM
Cyberman86
polar equations and vectors problem
This is not homework I'm studying for a test and i really tried this one i still doing it wrong.
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Use the Given information provided to find |(u+v)| and alpha
|u|= 21g
|v|= 3.2g
deita= 53 degrees

*Find the unit vector u in the direction of the vector w= <2 -1>

*Change the polar equation r= 4sin(deita) to rectangular form

*Use graphing techniques to sketch a graph of r= 2+2 cos(deita) on a polar coordinate plane. Show work and resulting graph.
• July 28th 2008, 12:24 PM
Mathstud28
Quote:

Originally Posted by Cyberman86

*Find the unit vector u in the direction of the vector w= <2 -1>

*Change the polar equation r= 4sin(deita) to rectangular form

$r=4\sin(\theta)$

$\Rightarrow{r^2=4r\sin(\theta)}$

$\Rightarrow{x^2+y^2=4y}$

$\Rightarrow{x^2+y^2-4y=0}$

$\Rightarrow{x^2+\left(y-2\right)^2=4}$

So its a circle of radius two centered at $(0,2)$

If $\bold{u}=\left\langle{}u_1,u_2\right\rangle$

Then

$\bold{\hat{u}}=\frac{\left\langle{}u_1,u_2\right\r angle}{\sqrt{u_1^2+u_2^2}}$

$\bold{\hat{u}}=\frac{\left\langle{}2,-1\right\rangle}{\sqrt{5}}$