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Math Help - how to translate point along given vector...

  1. #1
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    how to translate point along given vector...

    how to translate point along given vector...-trig_diagram.png
    here's the situation...

    the radius of the red circle is a given constant. point A can exist anywhere in any quadrant, but is always given... how would i calculate the coordinates of point B (the intersection of vector C with red circle).

    thanks!
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  2. #2
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    Re: how to translate point along given vector...

    Quote Originally Posted by wilbsy View Post
    Click image for larger version. 

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    the radius of the red circle is a given constant. point A can exist anywhere in any quadrant, but is always given... how would i calculate the coordinates of point B (the intersection of vector C with red circle).
    Suppose that the coordinates of A: (x,y).
    Suppose that x\cdot y\ne 0 then
     \Theta=Arg(x,y) = \left\{ {\begin{array}{{lr}}  {\arctan \left( {\frac{y}{x}} \right),}&{x > 0} \\   {\arctan \left( {\frac{y}{x}} \right) + \pi ,}&{x < 0\;\& \;y > 0} \\   {\arctan \left( {\frac{y}{x}} \right) - \pi ,}&{x < 0\;\& \;y < 0} \end{array}} \right.

    Then \Theta is the measure of the angle the vector \vec{C} makes with the positive x\text{-axis}~.

    Now the coordinates of B: (r\cos(\Theta),r\sin(\Theta)) where r is the radius of the circle.
    Thanks from LimpSpider and wilbsy
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