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Math Help - Finding parametric equations through a point and perpendicular to vectors

  1. #1
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    Finding parametric equations through a point and perpendicular to vectors

    Find parametric equations and symmetric equations for the line through a point Po(1,3,0) and perpendicular to vectors a and b.

    a = i + j
    b = j + k

    I need help finding out the parametric equations for this. In order to solve it would we need to cross a and b and then do the formula a + tv?

    where v is equal to axb.

    Thanks for your help.
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  2. #2
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    Re: Finding parametric equations through a point and perpendicular to vectors

    Quote Originally Posted by florx View Post
    Find parametric equations and symmetric equations for the line through a point Po(1,3,0) and perpendicular to vectors a and b.

    a = i + j
    b = j + k

    I need help finding out the parametric equations for this. In order to solve it would we need to cross a and b and then do the formula a + tv?

    where v is equal to axb.

    Thanks for your help.
    Are you told anything about vectors \displaystyle \textrm{a} or \displaystyle \textrm{b}, or are they arbitrary?
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    Re: Finding parametric equations through a point and perpendicular to vectors

    Quote Originally Posted by florx View Post
    Find parametric equations and symmetric equations for the line through a point Po(1,3,0) and perpendicular to vectors a and b.
    a = i + j
    b = j + k
    a\times b=i-j+k so the line is \begin{align*}x &=1+t\\y &=3-t\\z &=t   \end{align*}
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  4. #4
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    Re: Finding parametric equations through a point and perpendicular to vectors

    And, of course, you find the "symmetric equations" for the line by solving each of those for t and setting them equal.
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