Vector Field
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Scalar product
Definition The scalar product of two vectors p and q is defined to be [Equation goes here - download the original pdf to see it.] where [Equation goes here - download the original pdf to see it.] It can be shown that this definition is equivalent to [Equation goes here - download the original pdf to see it.] [Equation goes here - download the original pdf to see it.] Sometimes this second statement is taken as the definition of the scalar product. The scalar product is commutative This means [Equation goes here - download the original pdf to see it.] This follows from [Equation goes here - download the original pdf to see it.] since each of the products on the right is commutative. Scalar product and modulus (length) We have the relationship [Equation goes here - download the original pdf to see it. Proof [Equation goes here - download the original pdf to see it.] Distributivity of the scalar product over vector addition [Equation goes here - download the original pdf to see it.] Proof [Equation goes here - download the original pdf to see it.]
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Contents of
Vector Field
1 Scalar and Vector Algebra -Prerequisites
2 Formal definition of a vector
3 The position vector
4 About vectors
5 Orthonormal basis
6 Scalar product
7 Scalar invariant
8 Resolute of a vector
9 The cross (vector) product
10 Distributive law
11 Basis vectors
12 Area of the parallelogram
13 Parallel, anti-parallel
14 The triple scalar product
15 The triple vector product
16 Quadruple vector products
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