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Math Help - polar equations and vectors problem

  1. #1
    Junior Member Cyberman86's Avatar
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    Question 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.
    ___
    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.
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Cyberman86 View Post

    *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}}

    So in your case

    \bold{\hat{u}}=\frac{\left\langle{}2,-1\right\rangle}{\sqrt{5}}
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  3. #3
    Junior Member Cyberman86's Avatar
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    Question

    thanks for helping but is there a way you can post step by step using the formulas, I'm new on this and I'm really a visual learner.
    If you can't post the graph its ok, just the rest.
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