1. The problem statement, all variables and given/known data Find an equation of the plane that passes through the line of intersection of the two planes 3x + 7y + 2z= 0 and -9x - 8y - 6z = 9, and is perpendicular to the plane -2x - 6y + 3z = -10. 2. Relevant equations 3. The attempt at a solution Here is what I did: I first took the two normal vectors (n1 and n2) of the first two planes mentioned. n1 = (3, 7, 2) n2 = (-9, -8, -6) I then took the cross product of these two vectors: n1 × n2 = (-26, 0, 39) We can call this vector V. I then found the normal vector of the plane that is mentioned in the end of the problem (which I will denote as n3) n3 = (-2, -6, 3) Next I took the cross product between V and n3. V × n3 = (234, 0, 156) so then my normal vector for the plane that will be my solution is: nfinal = (234, 0, 156) I then found a point on the line of intersection in the plane by first setting z=0 and then solving a system of equations for x and y. Here is the system: 3x + 7y = 0 -9x - 8y = 9 solving for x and y yields: x = -189/117 , y= 9/13 (and of course z = 0) Now that I have my point and my direction vector, I can find the equation of the plane. I got: (234, 0, 156) ⋅ ( x + 189/117 , y - 9/13 , z) = 0 which expands to: (234x +378) + (0 - 0) + 156z = 0 which simplifies to 234x + 378 + 156z =0 or simply 234x + 156z = -378 That was the final answer that I plugged into the software for the equation of the desired plane. There were two answers that the problem wanted: They wanted the normal vector of the desired plane and the equation of the desired plane. When I plugged in my normal vector of (234, 0, 156) and my equation 234x + 156z = -378, the software said that I got the normal vector right, but got the equation wrong. Why?! I don't know what I did wrong here. Furthermore, I worked another example of this type of problem that simply had different numbers and equations with a friend earlier, and I got it right using the exact same process I used here! I've also looked up other examples of this online and every other example used the exact same process! Can someone please help me with this (because I am really ticked off and don't know what is wrong)?