What Good Are Dot Products?
- The dot product formula is easy to compute and gives you information about the angle between vectors.
- Many times you don't need an exact angle - it's often enough to know whether or not two vectors are perpendicular . (How could you tell this from the dot product?)
- The dot product formula has to do with two vectors. In general two vectors determine a plane. The formula extends directly to vectors in three-dimensional space (and even higher!).
- Physicists think (happily) that the dot product tells you about work.
If you have a constant force applied directly in the direction an object is moved, then the amount of work = (force)(distance).
If there is a constant force applied at an angle to the direction an object is moved, then the amount of work = (force) (distance), since this gives the component of force in the direction the object is being moved times the distance moved.
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