Question

PROJECTIONS Show that the plane pi and line of equation l are parallell and determine the distance

Answer 1

\[\pi = -3x + y - 4z = 1\]
\[\left(\begin{matrix}x \\ y\\z\end{matrix}\right) = \left(\begin{matrix}-4 \\ 7\\3\end{matrix}\right)+t\left(\begin{matrix}1 \\ -5\\-2\end{matrix}\right)\]

Answer 2

Try this one to get started.
http://www.netcomuk.co.uk/~jenolive/vect18b.html
then once you know it's parallel then let t=0 use that point on the line to find distance to plane. That is done by finding the projection of the line between a point on the line and a point on the plane onto the normal to the plane, then normalizing that. I'll find you a link that explains

Answer 3

thank you the first link helped tons. Is there like another visual example to help explain the second part better?

Answer 4

@dkebler

Answer 5

http://www.slideshare.net/leingang/lesson-4-lines-planes-and-the-distance-formula
try starting at page 55 of this slideshow

Answer 6

Internet is great for finding examples if you can figure out the search words. In this case I typed in "distance of a line to a plane".

Answer 7

whoops that's starting at page 50!