3D Vector proof (1 Viewer)

[James Smith The Third]

Hello friends, I am having trouble with part d of this question, any help would be appreciated!

8. The cube OABCDEFG has vertices O(0, 0, 0), A(a, 0, 0), B(a, a, 0), C(0, a, 0), D(0, a, a), E(0, 0, a), F(a, 0, a) and G(a, a, a), where a > 0.
(a) Use a scalar product to find the angle between the two face diagonals OF and OD.
(b) What type of special triangle is 4OFD?
(c) What special name is given to the triangular pyramid OBDF?
(d) Find 6 FXD, where X is the centre of the cube. (This angle is the bonding angle of carbon tetrachloride)

 

[Drongoski]

i remember doing a similar question in an IB Exam paper. can't find my old solution. I think the bonding angle is the same as that for methane: 109.5 degrees?

 

[Drongoski]

The centre of the cube is M(0.5a,0.5a,0.5a). Find the angle between vectors MA: (0.5a,-0.5a,-0.5a)' and MC: (-0.5a,0.5a,-0.5a)'.
You'll get the angle = 180 - inverse cosine of (1/3) = 109 deg 28 min.

Above not a direct response to your question.

 

[James Smith The Third]

The centre of the cube is M(0.5a,0.5a,0.5a). Find the angle between vectors MA: (0.5a,-0.5a,-0.5a)' and MC: (-0.5a,0.5a,-0.5a)'.
You'll get the angle = 180 - inverse cosine of (1/3) = 109 deg 28 min.

Above not a direct response to your question.

Ah that makes a lot of sense. Thanks for the help man appreciated