The line of intersection of the planes x + y + z = 1 and x + z = 0?

Question

Find parametric equations and symmetric equations for the line.

Answer 1

Find the normal vector for each plane. Take the cross product of the 2 normal vectors. This gives you the direction of the line. Find one point that is in both planes. Once you have the direction vector and a point the rest is a snap.

p.s. Why take the cross product of the normal vectors?.
1. The line of intersection is in each plane.
2. Every line in the plane is perpendicular to the normal.
3. The cross product of the normal vectors gives you a vector perpendicular to both normal vectors.
4. Since the cross product is perpendicular to both normal vectors it is on a line that is in both planes and therefore on the line of intersection.

Answer 2

y=1,
so x=-z
the line is the following:
(x,1,-x)

Answer 3

it all starts at zero,
three axis and zero is the starting point