Pick a point in the intersection: .
This cross product will give you the normal.
BTW the answer in the textbook is correct.
hello, I am studying for my exams and I came across a question that is really giving me trouble:
The planes: 2x + 3y + z = 2 and 5x - 2y + 2z = -4 are given. Find the scalar equation of the plane that contains the line of intersection of plane 1 and 2 and that passes through the origin.
I tried to use Ax + By + Cz + D + k(A2x + B2y + C2z + d2) = 0 but it didn't really seem to work out.
for quick reference:
scalar equation = ax + by + cz + d = 0
the answer at the back of the book is 9x + 4y + 4z = 0 but it might be wrong.
I will really appreciate some help.
Thanks a lot!!!
The line of intersection is found by solving the equations 2x + 3y + z = 2 and 5x - 2y + 2z = -4 simultaneously.
But you only need a point on this line. In other words, you only need one concrete solution from the infinite number of solutions available. So .....
Choose one of the variables, x say. Pick a convenient value for x, x = 0, say. Substitute x = 0 into the equations for the two planes. Solve the resulting equations simultaneously .....