Trigonometry/Vectors and Dot Products

From Wikibooks, open books for an open world
Jump to navigation Jump to search
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,


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