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Math Help - Equation of a line

  1. #1
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    Equation of a line

    Find vector equation for line

    2x-3y=1

    Can the answer be r=(1,1) + t(1,-2)

    Another important question will there always be an infinate number of answers for these questions??

    and any good tips to find vector equation of a line or even of a plane
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  2. #2
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    Quote Originally Posted by someone21 View Post
    Find vector equation for line

    2x-3y=1

    Can the answer be r=(1,1) + t(1,-2) Mr F says: Clearly not. t = 0 => r = i + j and the point given by this position vector, (1, 1), certainly doesn't lie on the line. However, r = 2 i + j + t (3 i + 2 j) is an answer ......

    Another important question will there always be an infinate number of answers for these questions?? Mr F says: Yes. For a line in the xy-plane, the answer has the form r = a i + b j + t (c i + d j) where (a, b) is any point on the line and c i + d j is any vector in the direction of the line. And there are an infinite number of points n the line ......

    and any good tips to find vector equation of a line or even of a plane Mr F says: Study as many examples as possible. Starting with the examples given in your class notes and textbook.
    ..
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    ..

    tying mistake

    r=(-1,-1)+ t(3,2)

    Can that be a answer???
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  4. #4
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    Quote Originally Posted by someone21 View Post
    tying mistake

    r=(-1,-1)+ t(3,2)

    Can that be a answer???
    Yes
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  5. #5
    Super Member wingless's Avatar
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    Quote Originally Posted by someone21 View Post
    tying mistake
    Hehe, you made a "tying mistake" there too
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