Vector Algebra
Some general Vector Algebra Formulas
Three-Vector (Cartesian coordinates)
General 3-Vector
 |
Eqn:C.1 |
References: Feynman II-2-5
Dot Product
 |
Eqn:C.2 |
note:
 |
Eqn:C.3 |
and:
 |
Eqn:C.4 |
References: Feynman II-2-2
Cross Product
 |
Eqn:C.5 |
 |
Eqn:C.6 |
where u is the unitNormal, a unit vector normal to the A,B plane, using right hand rule
References: Feynman II-2-2
Gradient
 |
Eqn:C.7 |
note:
is illegal |
Eqn:C.8 |
also known as: del, nabla
References: Feynman II-2-5,6
Divergence Operator
 |
Eqn:C.9 |
References: Feynman II-2-7
Curl Operator
 |
Eqn:C.10 |
References: Feynman II-2-8
Laplacian
 |
Eqn:C.11 |
 |
Eqn:C.12 |
References: Feynman II-2-10,11,12
Magnitude of A
 |
Eqn:C.13 |
References: Feynman II-2-9
Absolute Square
 |
Eqn:C.14 |
where,
is the complex conjugate |
References: Feynman
Complex Conjugate
is the complex conjugate |
Let
then,
where
Vector Formulas
 |
Eqn:C.15 |
 |
Eqn:C.16 |
 |
Eqn:C.17 |
 |
Eqn:C.18 |
 |
Eqn:C.19 |
References: Feynman II-2-9-11
See Also
References
- Feynman – The Feynman Lectures on Physics (volumes I,II,III), 1964