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.

F(x,y,z)

AF=BF from this x=y

AB=AF=BF=2

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

BF=

So

from the plane ABF

now x=y

So

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.

Thanks!