# Math Help - Vector problem involving two planes and point of origin!!!

1. ## Vector problem involving two planes and point of origin!!!

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!!!

2. Pick a point in the intersection: $\left( {0,1, - 1} \right)$.
This cross product $\left( {\left\langle {2,3,1} \right\rangle \times \left\langle {5, - 2,2} \right\rangle } \right) \times \left\langle {0,1, - 1} \right\rangle$ will give you the normal.

BTW the answer in the textbook is correct.

3. Originally Posted by Plato
Pick a point in the intersection: $\left( {0,1, - 1} \right)$...
How did you find that point?

4. Originally Posted by Morphayne
How did you find that point?
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 .....

5. Originally Posted by mr fantastic
Solve the resulting equations simultaneously .....
What does that mean? Use substitution/elimination?

6. Originally Posted by Morphayne
What does that mean? Use substitution/elimination?
Use whatever method you prefer.