 Home

Codex Wiki

List of universities

University of Oxford

Course of the University of Oxford

Undergraduate course of the University of Oxford

Physics course of the University of Oxford

Year 1 of the physics course of the University of Oxford

Mathematical methods I course of the University of Oxford

Past exam of the mathematical methods I course of the University of Oxford

2017

Write both <cross products> with the <Levi-Civita symbol>. Its contraction identity gives
$$
[a\times(b\times c)]_i=\epsilon_{ijk}\epsilon_{klm}a_jb_lc_m
=(\delta_{il}\delta_{jm}-\delta_{im}\delta_{jl})a_jb_lc_m
=b_i(a\cdot c)-c_i(a\cdot b).
$$
Therefore the <vector triple product> identity is
$$
\boxed{a\times(b\times c)=(a\cdot c)b-(a\cdot b)c.}
$$
The order matters: the <cross product> is not associative, and exchanging the two nested arrangements changes the expression.

Solution

Past exam of the mathematical methods I course of the University of Oxford / 2017 / 9 / b / Solution

Past exam of the mathematical methods I course of the University of Oxford / 2017 / 9 / b / Solution

 Ancestors (12)

 Discussion (0)

 Articles by others on the same topic (0)

Past exam of the mathematical methods I course of the University of Oxford / 2017 / 9 / b / Solution

 Ancestors (12)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)