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volcano5683
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Homework Statement
Could someone guide me to proof following equation.
For any A is a tensor; a, b, c are vectors. Proof that:
Tr (A) a.(b x c) = Aa.(b x c) + a.(Ab x c) + a. (b x Ac)
with (.) is dot product, and (x) is cross product of vector
Homework Equations
The Attempt at a Solution
My proof is below:
(1): Aa.(b x c) = Ai1(ei
similar to two remain part
(2): a.(Ab x c) = A22aiei. (bjej x ckek)
(3): a. (b x Ac) = A33aiei.(bjej x ckek)
from (1), (2), and (3) I get the result.
But there may have something wrong. Could anybody check for me?
Thanks