1. The problem statement, all variables and given/known data Find the cross product equation for the line L that forms the intersection of the planes: A: 2x - y + 2z = 1 and B: x + y - 2z = 1. 2. Relevant equations General equations for planes A and B: (a, b, and r are vectors). A: a dot r = 1 B: b dot r = 1 r = xi + yj + zk ; i, j, k here are the unit vectors. r X (b X a) = b - a alternatively, (b X a) X r = a - b 3. The attempt at a solution I only know one way in which to solve for the equation of a line intersecting two planes and that is to use the coefficients of the variables of x, y, and z to define two normal vectors, cross those normal vectors to get a parallel line to the intersecting line, then set x, y, or z equal to zero and solve the equations for x and y to define a point. Then, having a vector in the direction of the line (the cross product of the norms) and a point on the line, put it in the form r(t) = (position vector of point) + t(cross product of the norms). I solved the equation for the line in this way, but my teacher wants it as a "cross product equation." I have no clue how to get a and b to stick into the equations for the planes listed above. The only thing I could think of was using the coefficients of x, y, and z; but that makes no sense because that would be dotting a vector with its normal vector and the product would be 0, not 1. Does anyone have any ideas? The parametric equation I got for the line was r(t) = < 2/3, 1/3, 0, 6, 3 >, but this is not in the r X (b X a) form he wants it in. Thanks in advance.