# linear algebra – Since \$ operatorname {codim} partial M = 1 \$, then there are two orthogonal vectors \$ n_x in TM \$ that are orthogonal to \$ T ( partial M) \$

I am therefore studying the orientation of the boundaries (for example, Gulliemin and Pollack, page 97, Mukherjee, page 182) and it is stated that, in the first introduction,

$$dim M geq 1$$ is a smooth variety with limit and since $$codim partial M = 1$$ every $$x in partial M$$ there are two orthogonal vectors in the tangent space $$T_x (M)$$ at $$T_x ( partial M)$$ (one towards the inside and one towards the outside). I am 100% sure that it is only a trivial linear algebra.

Because if the remaining space has a dimension $$1$$, so it's a linear subspace. But how do we know that the rest would be orthogonal?