Question

In the methane molecule, CH4, each hydrogen atom is at a corner of a regular tetrahedron with the carbon atom at the center. In coordinates for which one of the C-H bonds is in the direction of i + j + k, an adjacent C-H bond is in the i - j - k direction. Calculate the angle between these two bonds.


I have a really hard time visualizing these things. I think it should be 60 degrees because the tetrahedron is divided into equilateral triangles..........is this right?

It's for the topic of vector addition...

Answer 1

https://www.mathsisfun.com/algebra/vectors-dot-product.html
A dot B = |A | |B| cos T
1*1 + 1*-1 + 1*-1 = 1 - 1 - 1 = -1
so
-1 = |A | |B| cos T
but
|A| = sqrt (1^2+1^2+1^2) = sqrt 3 and same for |B|
so
-1 = 3 cos T
cos T = -1/3
T = 109.5 degrees approx