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The scalar product of the vectors a and b is

(1.5) 
and, equivalently
Thus the scalar product is independent of the coordinate system.
The vector product is

(1.6) 
where is a unit vector perpendicular to both
and . The result is invariant with respect to the coordinate
system. In cartesian coordinates it is given by

(1.7) 
The easy way to learn this is to memorise the component and
the others are obtained by cyclic rotation of the subscripts,
The alternative method is to expand the determinant

(1.8) 
The triple scalar product is defined as

(1.9) 
The triple scalar product gives the volume of a parallelopiped formed
by sides defined by the vectors
and .
The triple vector product must be learnt. It is

(1.10) 
Similarly,
Next: Equation of Motion
Up: Introduction
Previous: Vector Fields and Fieldlines
Prof. Alan Hood
20001106