Calculating bond angles of a symmetrical tetrahedral molecule such as methane using a dot product
Consider the vectors U and V (with respective magnitudes |U| and |V|). If those vectors enclose an angle θ then the dot product of those vectors can be written as:
If the vectors can be written as:
then the dot product is given by:
We can interpret the last case by noting that the product is zero because the angle between the two vectors is 90 degrees.
this means that