Differential geometry

A curve β is said to be a plane curve if there exists a vector v such that for a fixed t1,
<β(t) - β(t1), v > = 0

Let r be a curve parametrized by arc length satisfying κ(s) ≠ 0 for any s.
Prove that r is a plane curve if and only if τ = 0.

* <a,b> = a dot b
κ = curvature of a curve
τ = torsion of a curve *