- #1

- 57

- 1

## Homework Statement

A line is given by the equation ##x + 2y - 3z = 7##.

Find any vector in the direction parallel to this line in the Cartesian coordinate system.

## Homework Equations

I imagine that there are some fundamental relationships I am missing here that would make this more comprehensible to me.

## The Attempt at a Solution

[/B]

Looking at the problem at the surface it would make much more sense if he had described the equation as a "plane" rather than as a "line," and if he were asking for a vector either orthogonal or parallel to the plane. As it is, it's quite confusing. I've been sifting through materials but I can't get past that this looks like the equation for a plane, not a line, and it's worded (and written) very specifically -- the notation above is the notation the professor used (no vectors, "hats," etc, but that notation appears in other questions immediately around this one, so I feel he omitted it on purpose).

What I think I want to do is convert this to a vector equation of a line in form

[itex]\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}}

\over r} = \left\langle {{x_0},{y_0},{z_0}} \right\rangle + t\left\langle {a,b,c} \right\rangle [/itex], but I'm not sure how to do that from this form.