This displacement is necessarily tangent to the curve at s, showing that the unit vector tangent to the curve is: u t ( s ) = [ x ′ ( s ) , y ′ ( s ) ] , while the outward unit vector normal to the curve is u n ( s ) = [ y ′ ( s ) , − − x ′ ( s ) ] , Orthogonality can be verified by showing the vector dot product is zero. The unit magnitude of these vectors is a consequence of Eq. 1.