Vectors
Because we will work with vectors it should be noted that there are two types of
multiplication of vectors - the dot product and the cross product. Geometrically,
the dot product of two vectors is the magnitude of one times the projection of the
other along the first. The symbol used to represent this operation is a small dot at
middle height (∙), which is where the name dot product comes from. Since this
product has magnitude only, it is also known as the scalar product.
(1) A ∙ Bi = AB cos β
where β is the angle between the two vectors.
Geometrically, the cross product of two vectors is the area of the parallelogram
between them. The symbol used to represent this operation is a large diagonal
cross (×), which is where the name cross product comes from. Since this product
has magnitude and direction, it is also known as the vector product.
(2) A × Bi = AB sinβn
where the vector n is a unit vector perpendicular to the plane formed by the two
vectors. The direction of П is determined by the right hand rule.
The right hand rule says that if you hold your right hand out flat with your fingers
pointing in the direction of the first vector and orient your palm so that you can
fold your fingers in the direction of the second vector then your thumb will point in
the direction of the cross product.
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