Engineering Statics

B-4


  Given the vectors P = -2i + 3j + 4k and Q = -i + 4j - 6k calculate the angle between vectors P and Q.

The dot or scalar product is defined the the product of 
the absolute values of the magnitudes of the two vectors times 
the cosine of the angle between them.
Rearranging terms allows you to solve for the cosine of the angle 
between the two vectors.

The magnitude of P is given by the square root of the sum of the squares of the components of P." >
The magnitude of Q is given by the square root of the sum of the 
squares of the components of Q.

The cosine of <font face=symbol>q</font> can then be found by substitution.
Arithmetic yields a value for the cosine of -.255.
The angle may then be found using the inverse or arcfunction 
on the calculator.  Notice that since the cosine is negative, the 
angle is more than 90 degrees.