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Math Help - Converting a Vector equation to a linear equation

  1. #1
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    Converting a Vector equation to a linear equation


    Here is a question from an assignment I am working on. The vector equation is easy.

    it is X = (1,2,1) + s(-3,-1,2) + t(3,-5,3).

    Everytime I try to get a linear equation out of it, I can get several equations, so I am not sure I am doing it right.

    My answer works out to be 7x+15y+18z = 125

    Can someone help me with this? Is my final answer correct?
    Last edited by lukasaurus; March 8th 2013 at 04:39 PM.
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  2. #2
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    Re: Converting a Vector equation to a linear equation

    Hey lukasaurus.

    By using Octave, I get a reduced system:

    >> >> X = [1,2,1; -2,1,3; 4,-3,4]
    X =

    1 2 1
    -2 1 3
    4 -3 4

    >> rref(X)
    ans =

    1 0 0
    0 1 0
    0 0 1

    This confirms your answer to be correct.
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  3. #3
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    Re: Converting a Vector equation to a linear equation

    Thanks, but I am not sure how this confirms my answer to be correcT?

    edit : it isn't correct - the last value - 125, should have been 55. I must have done a miscalc somewhere.
    Last edited by lukasaurus; March 8th 2013 at 05:19 PM.
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  4. #4
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    Re: Converting a Vector equation to a linear equation

    Quote Originally Posted by lukasaurus View Post

    Here is a question from an assignment I am working on. The vector equation is easy.
    Having taught this material for many years, I do not like your approach.
    Here is mine. Let R=(x,y,x). Then your plane is
    \left[ {\overrightarrow {AB}  \times \overrightarrow {AC} } \right] \cdot \left( {R - C} \right) = 0
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  5. #5
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    Re: Converting a Vector equation to a linear equation

    Unfortunately, the assignment requires me to use the method taught for both the vector and linear equations. I'm new to this. I got an A on the summer school paper and I haven't done maths for about 10 years (as a subject at least), so all the terminology is new. This is a Level 1 paper (first year) on Linear Algebra and Vectors. I don't really understand what your method is saying?
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  6. #6
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    Re: Converting a Vector equation to a linear equation

    Lukasaurus, Plato is absolutely right. That approach is logical and easy to understand. once one gets vector equation one can easily find the linear equation.
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  7. #7
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    Re: Converting a Vector equation to a linear equation

    Can you give an example of how this is worked out on paper?
    how do you do AB * AC. If both are 3x1 matrices, how can they multiply?
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  8. #8
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    Re: Converting a Vector equation to a linear equation

    Vector AB = -3i -j +2k and vector AC = 3i-5j+3k
    AB x AC = 7i+15j+18k and R-C = (x-4)i+(y+3)j+(z-4)k
    Find (ABxAC). ( R-C)=0
    Now i am sure you would be able to complete the solution
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