My name is Lindsay. I am an OAC student (which is the Ontario equivalent to Grade 12 in most other states and provinces). I am in an Algebra and Geometry course and am currently studying a unit on equations of planes. Our teacher has given us this question that my friend and I have attempted several times, but we are still unable to solve it. My teacher has also suggested using the internet as a resource. The question is:
Prove that a necessary condition that the three planes
-x + ay + bz = 0 ax - y + cz = 0 bx + cy - z = 0have a line in common is that
a^2 + b^2 + c^2 + 2abc = 1
Thank you very much.
Here is are two approaches:
Take two of the planes and find the line of intersection.
Now take the points on this line of intersection and
substitute them into the third equation.
If they fit the third equation - then the three planes
share the line.
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