EXAMPLE 4.1.2: DOT PRODUCT: ANGLE BETWEEN VECTORS

With the same given situation, determine the cable between cable AC and strut AO.

The same procedure is to be used in solving for the angle between the other cable AC and strut AO. The working equation used is still:

                                                    

However, the difference of this example from the previous one is the determination of the coordinates of the three points in consideration. Notice that point C has an angle and the direct distance of the point from point O, thus, we should break the 5-ft distance into its -x and -z components to the have coordinates.

POINTS	i, ft	j, ft	k, ft
A	0	6	2
C	5cos60=2.5	0	5sin60=4.33
O	0	0	0

The properties of strut AO will remain the same from the previous example.

      and

Solve for the parameters of vector AC.






Take the scalar of vector AC.





Take the Dot Product of the two vectors:






Substitute the known parameters to the working equation:

      ANSWER

Back to 4.1. INTRODUCTION TO DOT PRODUCT