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Math Help - Vectors!

  1. #1
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    Vectors!

    1.) P(-1,2,3) and Q(4,0,1) are two points in space. Find the angle that PQ makes with the X-axis.

    I got PQ to be (5,-2,-4). I know to use the formula for the angle between two vectors but I'm having trouble with the x-axis part. I know it is k(1,0,0), where k is a parameter. Since (1,0,0) is a direction on the x-axis, to have a line, k would be a parameter.
    But with this unknown parameter, how am I to solve for the angle?

    2.) Given P(2,-5,6) and Q(-1,7,9), find the distance from P to the x-axis.
    Again the parameter problem, I can solve it without the parameter, so how should I go about this question?


    3.) For A(2,-1,3) and B(0,1,-1), find the coordinates of C on AB which is 2 units from A.

    How do I do this? I know it is something to do with ratio but I'm not sure..



    Thank you so much!
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    Re: Vectors!

    1. You need to use the definition of the dot product: \displaystyle \begin{align*} \mathbf{a} \cdot \mathbf{b} = \left| \mathbf{a} \right| \left| \mathbf{b} \right| \cos{\left( \theta \right)} \end{align*}.

    2. Why would you be given Q if you are just finding the distance between P and the x axis? Did you write this question correctly?
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    Re: Vectors!

    Hi thank you for your reply! For 1.) I know to use the dot product but please how do I do it? I really am unsure of what to do with the parameter since the x axis is k(1,0,0) where k is a parameter! For2.) I copied the question correctly, it is just that there are other parts to this question that involves Q that I know how to do this I didn't put them down.
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    Re: Vectors!

    Quote Originally Posted by Tutu View Post
    Hi thank you for your reply! For 1.) I know to use the dot product but please how do I do it? I really am unsure of what to do with the parameter since the x axis is k(1,0,0) where k is a parameter!
    Do nothing with it.
    The answer is simply \arccos \left( {\frac{{\overrightarrow {PQ}  \cdot i}}{{\left\| {\overrightarrow {PQ} } \right\|}}} \right)
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    Re: Vectors!

    Is there a value.for i? Like 1 or something
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    Re: Vectors!

    Quote Originally Posted by Tutu View Post
    Is there a value.for i? Like 1 or something
    If you know nothing about this subject, why are you doing these problems?

    i=<1,0,0>.
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    Re: Vectors!

    Quote Originally Posted by Tutu View Post
    Hi thank you for your reply! For 1.) I know to use the dot product but please how do I do it? I really am unsure of what to do with the parameter since the x axis is k(1,0,0) where k is a parameter! For2.) I copied the question correctly, it is just that there are other parts to this question that involves Q that I know how to do this I didn't put them down.
    Work out the dot product, work out the magnitudes of the vectors, substitute them in, then solve for theta.
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