Vector Products
- Vectors are not ordinary numbers so normal multiplication has no direct analog. None the less, there are two way to "multiply" two vectors which are useful in physics.
- The scalar or dot product "multiplication" of two vectors produces a single number plus units. The form of the dot product is:
- The vector or cross product "multiplication" of two vectors produces a new single vector plus units. The form of the cross product is:
Dot Product: 
- The dot product takes one of the vectors and projects its length onto the other vector. This projected length is then multiplied by length of the other vector to produce the value of the dot product. You get the same results no matter which vector you project onto the other.
- In the most trivial case the dot product of two vectors that are in the same direction is just the product of the magnitudes of the two vectors. On the other hand, if the vectors are at right angles to each other their dot product is zero.
Vector (or Cross) Product: 
- The magnitude of the cross product is equal to the area of a parallelogram formed using the vectors as the sides of a parallelogram.
- The direction of the cross product is perpendicular to the plane formed by the two vectors and follows the right hand rule.
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