Simplify With Assumptions Not Using Distributive Property Of Dot Product

Question

Given the following expression

Assuming[(n | d | t) ∈ Vectors[3, Reals] && n.t == 0, FullSimplify[(n + d).t]]

Why does mathematica give me the below instead of simplifying to d.t?

(d + n).t

Answer 1

You can add TensorExpand to achieve this:

Assuming[(n | d | t) ∈ Vectors[3, Reals] && n.t == 0, 
   TensorExpand[(n + d).t] // FullSimplify]

(* d.t *)

As I understand it, manipulating symbolic tensors should generally be done with the Tensor* family of functions (guide page). This is not built-in in functions like FullSimplify .