The cross section of a right prism is an equilateral triangle. The rectangular face ABCD of the prism lies on the plane , where A and B are the points and respectively. EF is the edge in which the other two rectangular faces ADEF and BCEF meet.
Prove that the equation of the plane containing A, B, F is
If the origin lies inside the prism, determine the equations of the line EF.
I have proven the first part, but I can't get the equations of EF.
AF=BF from this x=y
Perpendicular distance of F from plane ABCD=
Where is the angle of elevation of F from A.
Fill in the values for the perpendicular distance.
Then we have
from the plane ABF
The direction ratios of the line are 5:5:-2 since it is perpendicular to the plane ABF
the equations for the line I arrive at are
the answer is supposed to be
I can't find where I'm wrong.