WeBWorK Problems

vector problem request

vector problem request

by Zak Zarychta -
Number of replies: 3
Having perused the repositories for questions about vectors i see a lot of ijk style vector questions and a couple of vector questions related to the vector equation of planes in Cartesian form. eg

 Find a vector \vec v parallel to the intersection of the planes x-4y-4z = 2 and 2y-2x-z = 7.

As i am in a bit of a pinch regarding time for development. I was wondering if anyone has developed (and is prepared to share with me) questions relating to the general vector form of;

equations for a lines in 2d of the form (please excuse the TeX)
\bm{l} = \vec{OA} + \lambda \vec{AB}

such as
\bm{l} =  <2,-1> + \lambda <2,4> 

and planes in 3d
\bm{p} = \vec{OA} + \lambda \vec{AB} +  \mu \vec{AC}

such as
\bm{p} =  <4,2,0> + \lambda <-1,-1,1> +  \mu <0,-3,1>

In reply to Zak Zarychta

Re: vector problem request

by Davide Cervone -
There are a few problems on parametric lines in the Union library under the directory setMVlinesplanes. I don't think there are any on parametric planes, though (just implicit planes).
In reply to Davide Cervone

Re: vector problem request

by Zak Zarychta -
That's great Davide it'll give me some material to work with, many thanks.
Zak
In reply to Zak Zarychta

Re: vector problem request

by Davide Cervone -
I realized that there isn't currently a pre-defined checker for parametric planes (though there is one for parametric lines). So I've put together a macro file for a new ParametricPlane object that works like the ParametricLine object. I've attached the macro file for it. There are comments at the top, but it should allow you to ask questions about parametric planes similar to those about parametric lines in the problems I mentioned.

Currently, this file only works with planes in 3-space (because it uses a cross product internally). I haven't taken time to try to work out a more general comparison mechanism, but I hope that is sufficient for your needs.

Davide