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calculus vector help pleeeeease

Hey peeps,

I have an assignment that I just can't figure out.
The introduction is

A molecule of methane, CH4, forms a regular tetrahedron
with the four hydrogen atoms at the vertices and the carbon
atom at the centroid. Let the vertices of the first three
hydrogen atoms be (1, 0, 0), (0, 1, 0), and (0, 0, 1)

I'm stuck on part D-F

d) Determine the coordinates of the fourth hydrogen
atom using the condition that all hydrogen atoms
must be equidistant.
(e) Determine the coordinates of the carbon atom by
computing the “average” position of the four hydrogen
atoms (i.e., add the hydrogen position vectors and
divide by 4).
(f) Compute the bond angle, i.e., the angle between the
lines that join the carbon atom to two of the hydrogen
atoms.

If anyone has any suggestions how I can tackle any of these I'd be really grateful!!!

Thanks!

Edit: actually I think I found part D as (0.5,0.5,0.5)

(edited 11 years ago)

Reply 1

ghostwalker

Original post by Scotty Bear

Edit: actually I think I found part D as (0.5,0.5,0.5)

You might like to check the distances with that as your 4th set of coordinates.

PS: Is this assessed work?

Reply 2

Scotty Bear

No it's just our weekly homework.

It's (1,1,1) not 0.5 right.

Reply 3

ghostwalker

Original post by Scotty Bear

No it's just our weekly homework.

Cool. As we're not allowed to help with assessed work.

It's (1,1,1) not 0.5 right.

The three given points define a plane, and there will be two possibilities for the fourth point, such that all four are equidistant.

(1,1,1) is one of them.

Reply 4

ghostwalker

Part (e) is straight forward for you, I presume.

For part (f), you could use the dot product, if you've covered it.
Or, use the cosine rule, on a triangle consisting of the carbon atom, and any two of the hydrogens.