# Math Help - Vector Product #2

1. ## Vector Product #2

Find the equation of the plane which passes through the point (1,2,3) and contains the line of intersection of the planes 2x-y+z=4 and x+y+z=4.

thank you.

2. What ideas have you had so far?

3. vector product the two planes?

$\begin{pmatrix}
2\\
-1\\
1
\end{pmatrix}\begin{pmatrix}
1\\
1\\
1
\end{pmatrix}$

4. Hmm. Well, in order to define a plane, you need a normal vector, and a point in the plane. You have the point. How could you get a normal vector?

5. Dot Product (1,2,3) with $\begin{pmatrix}
2\\
-1\\
1
\end{pmatrix}$

??

6. You're guessing. You need to think geometrically here. You've got one point on the plane, and, given the equations you have, you could generate the equation for a line in the plane. But to write down the equation for a plane, you need a line normal, or perpendicular, to the plane. How can you get that line?

7. solved it
by following the example