Expert: Steve Holleran - 2/26/2008

Question
What is the dot product of the two displacement vectors U=[2m,-1m,3m] and W=[5m,2m,-2m]? What is the angle between these vectors?

Answer
Hi Lidia,

Okay, the dot product formula is

             U . W = |U| |W| cos A  where A is the angle between the vectors.

Now, the dot product is what you get by multiplying the corresponding components:

  U . W = 2m * 5m + -1m * 2m + 3m * -2m = 2m^2

 |U| = sqrt(4m^2 + m^2 + 9m^2) = m * sqrt(14)

 |W| = sqrt(25m^2 + 4m^2 + 4m^2) = m * sqrt(33)

So then you have :

             2m^2 = m * sqrt(14) * m * sqrt(33) * cos A

or             2 = sqrt(14) * sqrt(33) * cos A

so             2 = sqrt(462) * cos A

and            A = Arccos(2/sqrt(462)) = 1.4776 radians

Hope this is what you needed.

Steve