How do you find the line of intersection of two planes?

Question

How do you get it into parametric form?

Answer 1

How do you find the line of intersection of two planes?
Well, in 3-D a linear equation, in which the orders of x, y and z do not exceed 1, represents a plane. When you have two planes, you must have two linear equations. The combination of these two linear equation represents a straight line.

How do you get it into parametric form?
When you have two 3-variable (x,y and z) equations (as I stated above), you should have infinite number of solutions, representing points on the line. You may arbitrarily pick two different solutions, (x1,y1, z1) and (x2,y2,z2), representing two points on the line. Imagine that you are moving from the first point to the second point in a uniform speed. Hence the parametric form can be written as:
x = x1 + (x2 - x1)t
y = y1 + (y2 - y1)t
z = z1 + (z2 - z1)t
where x1,x2,y1,y2,z1,& z2 are all numbers, t the parameter introduced in as an additional variable, and hence we have 3 equations.