# Binormal vector

## Main Question or Discussion Point

How can I show that the binormal vector is orthogonal to the tangent and normal vector. I know i should use the dot product to determine this, however i do i actually go about doing it?

MathematicalPhysicist
Gold Member
Well, if T is the tangent vector, N the normal to T, and B=TxN (cross product of the two), then you should use the fact that a*(bxc)=det[a,b,c] where * is the dot product.
I.e it equals the determinant of the vectors (in rows) a,b and c.

Hurkyl
Staff Emeritus
Gold Member
How can I show that the binormal vector is orthogonal to the tangent and normal vector.
Isn't that (most of) the definition of the binormal vector?

Maybe you're using a different exposition than I would expect -- what definition of "binormal vector" is your class using?

this was a problem in a my book. MathematicalPhysicist, that is what i want to do however is there a way to show it is perpendicular without any specific values for the components of the vector?

mathman