In doing multivariable calculus, I read
Okay, we know that we need a point and vector parallel to the line in order to write down the equation of the line. In this case neither has been given to us.
First let’s note that any point on the line of intersection must also therefore be in both planes and it’s actually pretty simple to find such a point. Whatever our line of intersection is it must intersect at least one of the coordinate planes. It doesn’t have to intersect all three of the coordinate planes but it will have to intersect at least one.
This quote comes form an explanation in how to find the equation of a line from the intersection of two planes.
What confused me was the idea that no matter what, a line MUST intersect at least one coordinate plane. This was weird to me as I've seen examples where there is a point P(2, 3, 4) and another point Q(3, 4, 5) and I know that the line between them do not touch upon any coordinate planes where x,y, or z is 0.
Therefore, how is this statement true?
My guess would be that we are assuming that the equation of the line of intersection between two well defined planes is infinite? By defined planes, I mean that the planes take up a certain amount of space and aren't infinite.