The line is not perpendicular to the intersection, the line IS the intersection...
Find the equation of the plane passing through the intersection of and and passing through
I forgot how these sums are done:Here's what I did:
solving the two equations we get and
hence we get the parametric equation:
hence the direction vectors=
as the line is perpendicular to the intersection, it is also the normal vector of the 3rd plane:
equation of required plane:
putting we get
new simplified equation:
but the answer given in the book is:
What am I doing wrong here?
thanks in advance.
You don't need to. Just choose two points that you know lie on the line, and use the point you are told lies on the plane, to substitute into the plane equation ax + by + cz = d. You will get three equations in three unknowns to solve simultaneously.