Breaking down the equation of a plane Could someone explain the individual parts of a plane equation?
For example:
$3x + y + z = 7$
When I see this I can't imagine what it's supposed to look like.

Consider the collection of vectors $\{\vec x:\vec x\perp (3\vec i+\vec j+\vec k)\}$.  The endpoints of these form a plane through the origin.  If you shift this plane upwards $7$ units, you get the plane in question.
