Find the parametric equations of the intersection of the planes x + (y − 5) + z = 0 and −x + (y + 5) − z = 0. (use the parameter t. enter your answers as a comma-separated list of equations.)

The cross product of the normals to the planes is [1, 1, 1] × [-1, 1, -1] = [-2, 0, 2], so the direction vector of the line of intersection can be written as <1, 0, -1>. A point on the line of intersection can be found to be <5, 0, 0>, so one possible set of parametric equations for the line of intersection is
.. = <5 +t, 0, -t>