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t[s], n[s] and b[s] are three orthogonal vectors. I define a cross product Cross[t[s], n[s]] = b[s]. I want to calculate the cross product in the formula a2, I want a2 to have the same result as a3. How to achieve this?

Cross product of two unknown orthogonal vectors

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1 Answer 1

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Setting UpValues for n gives desired result:

n /: Cross[(a_. t[s]), n[s]] := a b[s]

(2 q[s] T1) t[s]\[Cross]n[s]
(* 2 T1 b[s] q[s] *)

(2 t[s] q[s] T1)\[Cross]n[s]
(* 2 T1 b[s] q[s] *)
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  • $\begingroup$ Thank you for your excellent answer! $\endgroup$
    – Yang Liu
    Sep 9, 2019 at 3:15
  • $\begingroup$ If you like answer you can accept it, but of course I do not insist. $\endgroup$
    – Alx
    Sep 9, 2019 at 7:58

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