Unit Normal Vector - Three Dimensional Space

The unit normal vector is illustrated to be,

N (t) = ^→T' (t) / (|| T^→' (t)||)

The unit normal is orthogonal or normal or perpendicular to the unit tangent vector and therefore to the curve also.  We have already seen normal vectors while we were dealing with Equations of Planes. They will come up with some regularity in several Calculus III topics.

The definition of the unit normal vector all time seems a little mysterious while you first see it.  It follows directly from the subsequent fact.

Fact

Assume that r^→ (t) is a vector like || r^→ (t)|| = c for all t. Then ^→r' (t) is orthogonal to r^→ (t)