# The Vector Equation of a Plane

• Mar 29th 2009, 09:16 AM
Erghhh
The Vector Equation of a Plane
Find the eqn of the plane in the form r.n=p, which contains the line, l, and the point with position vector, a, where

l: r=-2i +3j-k +t(2i-j-3k) a=-3i+j+2k

Any help on working out n?
• Mar 29th 2009, 09:28 AM
Plato
$\begin{gathered}
n = \left\langle {2, - 1, - 3} \right\rangle \times \left\langle {-3 + 2,1 - 3,2 + 1} \right\rangle \hfill \\
\Pi :n \cdot \left\langle {x - 3,y - 1,z - 2} \right\rangle = 0 \hfill \\
\end{gathered}$
• Mar 29th 2009, 09:37 AM
Erghhh
I'm not sure i understand; the answer in the back of my book tells me it's r.(9i+3j+5k)=-14
• Mar 29th 2009, 10:37 AM
Quote:

Originally Posted by Erghhh
Find the eqn of the plane in the form r.n=p, which contains the line, l, and the point with position vector, a, where

l: r=-2i +3j-k +t(2i-j-3k) a=-3i+j+2k

Any help on working out n?

Ok what should be the plane's direction?

What should be its distance from origin?
think in terms of line and that point :)

EDIT: Distance = perpendicular distance of plane