Vector triple product
; the operation is not associative.
Expansion identity
Proposition 2.25
For , we have
Proof by index notation
With index notation and the contraction , the th component of the left-hand side is
which is precisely the th component of the right-hand side.
Non-associativity
The vector triple product is not associative:
Related
Stated in
- Definition 2.24 (Vector Triple Product)§2.5.2 Vector Triple Product
- Proposition 2.25§2.5.2 Vector Triple Product