DOT PRODUCT (AKA inner product or scalar product)

We say "A dot B" and write A× B. (In quantum mechanics it is
<Aô B>.)
Two ways to do it:

1. The product of magnitudes times the cosine of the angle between them.

2. The sum of the products of their corresponding components. ( Multiply x components, multiply y components, multiply z components, then add all three products.)

The cosine factor provides a measure of the "agreement" or parallelism between the two vectors. The cosine can be anything from +1 to -1: It is +1 for parallel, 0 for perpendicular, and -1 for anti-parallel. Another way to look at it is that the dot product is the magnitude of one vector times the component of the other in the direction of the first.

Example: If A is (1, 5, -3) and B is (-4, 3, -2) then the dot product is -4+15+6 = 17. Note that you can find the magnitudes of A and B, then solve for the angle between them: the magnitudes are the square roots of 35 and 29, respectively, so cosine of the angle between them is 17/(1015)^1/2.

Work done by a force is the dot product of the force acting on a body and the displacement of the body that occurs while the force acts.

You could wear the scalar product of polka and shirt. Aarrgh to escape to vectors. @$#%^& to escape to work & energy.

Or go to one of the main physics pages:
Mechanics
Fluids, heat, electricity and magnetism
Vibrations and waves
Quantum
Index

Comments, questions: fredrick.gram at tri-c.edu (remove spaces and replace at with @. This is my defense against spammer software that gets email addresses that are listed on the web).