Vector Algebra

Some general Vector Algebra Formulas

Three-Vector (Cartesian coordinates)

Contents

General 3-Vector

25e00e754198f3d660cbe9d9c77dfbf9.png Eqn:C.1

References: Feynman II-2-5

Dot Product

ee0f7af16b4e954bf9dba2f4a306c696.png Eqn:C.2

note:

a800c3cd9c7715b100cbe0eb2c57dbaf.png Eqn:C.3

and:

8bffe8ef7f3b9fcba002994c2a6888f9.png Eqn:C.4

References: Feynman II-2-2

Cross Product

5357273e2b25e5d05e924adcf944a7f9.png Eqn:C.5
d0750999c1bde020787286f00f05fb78.png 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

ff40ce40cc4ddc27bafea0332eb6f4f2.png Eqn:C.7

note:

e521ee229df4d8e376132bff3dd42067.pngis illegal Eqn:C.8

also known as: del, nabla

References: Feynman II-2-5,6

Divergence Operator

05a0dd09d24423417e1641b963f6243b.png Eqn:C.9

References: Feynman II-2-7

Curl Operator

f644370995c8da7d9b1e52e19cd01704.png Eqn:C.10

References: Feynman II-2-8

Laplacian

fd138871a572e9636ac9a33355be504c.png Eqn:C.11
3080a2b4d7717e1b156000f1f395e356.png Eqn:C.12

References: Feynman II-2-10,11,12

Magnitude of A

40038341f3322cc2012303815e90441a.png Eqn:C.13

References: Feynman II-2-9

Absolute Square

09f8433cb45d609761f7aefe8983d987.png Eqn:C.14

where,

d5159810036b1f1348a59f11bec67edf.pngis the complex conjugate

References: Feynman

Complex Conjugate

f908c00dc2374217cca8a13b8d9725bf.pngis the complex conjugate

Let

3b47452170e6417ee2e5d4620a92a70f.png

then,

99f690922815d7e6f81fd80491f3d823.png

where

dd9cdd5fb37cd89555826836ed94d2d9.png

Vector Formulas

ffb47d0d5500739dbcd8eb7a91b9b472.png Eqn:C.15
b449ed016e51719f1e15d003c9dac0ea.png Eqn:C.16
977c739d4f276780c0d4ddfaff9c29a0.png Eqn:C.17
2337334ab92488a83fa14e1d0aa9d6da.png Eqn:C.18
70cbbbfd2888b6ced8838549a65c3648.png Eqn:C.19
49207f94bfd82a08dcd957d2eb493f0f.png Eqn:C.20

References: Feynman II-2-9-11

See Also

References