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Math Help - Is this Vector proof correct?

  1. #1
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    Is this Vector proof correct?

    Prove that the point A (i+2j-3k) lies on the line L1 <br />
r = \left(\begin{array}{c}4\\-4\\3\end{array}\right) + \mu \left(\begin{array}{c}1\\-2\\2\end{array}\right)<br />

    So what i have done is:

    \left(\begin{array}{c}1\\2\\-3\end{array}\right) = \left(\begin{array}{c}4\\-4\\3\end{array}\right) + \mu \left(\begin{array}{c}1\\-2\\2\end{array}\right)

    \left(\begin{array}{c}1\\2\\-3\end{array}\right) - \left(\begin{array}{c}4\\-4\\3\end{array}\right) = \mu \left(\begin{array}{c}1\\-2\\2\end{array}\right)

    \left(\begin{array}{c}-3\\6\\-6\end{array}\right) = \mu \left(\begin{array}{c}1\\-2\\2\end{array}\right)

    Therefore: \mu = -3

    so Point A deos lie on the line L1.

    am not sure if this is the correct way to prove it.
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  2. #2
    Moo
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    Hello Fedex,



    Use ImageShack&#174; - Image Hosting to upload your pictures online.

    Then take the url of the pic and use the [img] things


    Otherwise, you can click on "manage attachments", right below options, which are below the window where you type your message.
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  3. #3
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    Yep. Spot on. The point is that the equations:

    \left(\begin{array}{c}-3\\6\\-6\end{array}\right) = \mu \left(\begin{array}{c}1\\-2\\2\end{array}\right)

    [/quote]

    Give you the SAME value of mu. So the equations are consistent, so the point is on the line.

    That's as good a way as any to prove it.
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  4. #4
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    Hey Moo,

    Thanks :-) I tried to copy and paste a formula, but I accidentally copied and pasted a picture. Pretty silly of me, but I sorted it now.

    Thanks, though :-)
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  5. #5
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    Thank You

    The next part fo the question goes on to say:

    The point C (2i-k) lies on the line L2

    Find the shortest distance from C to L1.

    L1: r = \left(\begin{array}{c}1\\2\\-3\end{array}\right) + \lambda \left(\begin{array}{c}4\\-5\\-3\end{array}\right)

    L2: r = \left(\begin{array}{c}4\\-4\\3\end{array}\right) + \mu \left(\begin{array}{c}1\\-2\\2\end{array}\right)

    How would i go abou finding the shortest distance?
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