Open main menu

Trigonometry/Vectors and Dot Products

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:

For example,

and

We can interpret the last case by noting that the product is zero because the angle between the two vectors is 90 degrees.

Since

and

this means that