# Thread:

1. ## 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.

2. Originally Posted by free_to_fly
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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