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FP3 the angle between 2 faces of a tetrahedron vectors

http://www.ocr.org.uk/Images/61390-question-paper-unit-4727-01-further-pure-mathematics-3.pdf question 5iii , mark scheme http://www.ocr.org.uk/Images/57748-mark-scheme-january.pdf

am i right in saying the angle between 2 plane faces of a tetrahedron is 180-the angle between the normal of the planes? which i saw an example of in my textbook

on the mark scheme it just does the cosine of the angle between the 2 normals of the plane, which means that the angle between the plane is the same as the angle between the 2 normals?
Original post by physics4ever
http://www.ocr.org.uk/Images/61390-question-paper-unit-4727-01-further-pure-mathematics-3.pdf question 5iii , mark scheme http://www.ocr.org.uk/Images/57748-mark-scheme-january.pdf

am i right in saying the angle between 2 plane faces of a tetrahedron is 180-the angle between the normal of the planes? which i saw an example of in my textbook


Yes.


on the mark scheme it just does the cosine of the angle between the 2 normals of the plane, which means that the angle between the plane is the same as the angle between the 2 normals?


Notice that they have taken the modulus of the dot product, which deals with the 180 minus part. The dot product itself will be negative, and taking the modulus gives the 180 minus part.

Based on the idea cos x = - cos (180-x)
Original post by ghostwalker
Yes.



Notice that they have taken the modulus of the dot product, which deals with the 180 minus part. The dot product itself will be negative, and taking the modulus gives the 180 minus part.

Based on the idea cos x = - cos (180-x)

ahh right thanks!

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