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ABCD is a regular tetrahedron, i.e. its sides are of equal length. E and F are the mid-points of AB and CD respectively. Find the angle between
a) the plane ABEF and the plane CDEF
b) the plane ABEF and the line AC
c)the line AC and the line EF
Can anyone help me?
http://www.p1cture.it/images/d8ffeca5d82b71a3cfb3.png
[Just picture it as a triangular pyramid with all sides equal]
I think that the first question can be answered without any calculation. (red and blue lines to show the two planes CDEF and ABEF respectively, better)
For the second one, I suggest you assign some coordinates to the tetrahedron and use the equation of the line AC with the normal of the plane ABEF.
For the last one, it can be seen that the line AC (broken line) and line EF (green line) don't meet in the 3D space.