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Math Help - Locus of points

  1. #1
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    Locus of points

    Q: Describe the locus of points that satisfy the equation:
    <br />
r \wedge a = b<br />
    where <br />
\begin{array}{l}<br />
 a = (1,1,0) \\ <br />
 b = (1, - 1,0) \\ <br />
 \end{array}<br />
.

    My thinking was that the locus is either a line or a plane, where b is perpendicular to a, but I'm not entirely sure which one it is. Help would be loved.
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  2. #2
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    Quote Originally Posted by free_to_fly View Post
    Q: Describe the locus of points that satisfy the equation:
    <br />
r \wedge a = b<br />
    where <br />
\begin{array}{l}<br />
a = (1,1,0) \\ <br />
b = (1, - 1,0) \\ <br />
\end{array}<br />
.

    My thinking was that the locus is either a line or a plane, where b is perpendicular to a, but I'm not entirely sure which one it is. Help would be loved.
    There are probably better ways than this:

    Let r = <\alpha, \, \beta, \, \gamma>.

    Then r \wedge a = <-\gamma, \, \gamma, \, (\alpha - \beta)>.

    Therefore r = <\alpha, \, \alpha, \, -1> = <0, \, 0, \, -1> + \alpha <1, 1, 0> for all real values of \alpha.

    This is the vector equation of a line.
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