EXAMPLE 4.1.1: DOT PRODUCT: ANGLE BETWEEN VECTORS

From the given situation, determine the cable between cable AB and strut AO.

Consider strut AO and cable AB as the two vectors. There are three points of consideration in the Cartesian plane. The following table shows the coordinates of those three points in the -x, -y, and -z axes (i, j, k)

POINTS	i, ft	j, ft	k, ft
A	0	6	2
B	3	0	4
O	0	0	0

The dot product formula to measure the angle between these vectors is:

                                                          

Although  is a given, this is but the scalar quantity of the force. In order to solve for the angle between, the vector representations are required (instead of the magnitude of the force). Convert the force into its Cartesian representation:

Then take the scalar of force AB:




Do the same procedure for strut AO:






For the scalar of  strut AO:




Take the Dot Product of the vectors:






With all parameters known, let's go back to the working equation to solve for the angle between the vectors:




          ANSWER


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