Monotonicity of vector fields

If I have a vector field (x,y,z) on a one dimensional line (x-axis) and if I have to check its monotonicity between two intervals. Will it be monotonic if:

(1) only one of the components of vector field is monotonic in that interval. OR (2) two of the components of vector field are monotonicaly increasing and the other is monotonicaly decreasing in that interval. OR (3) all the components of vector field are either monotonicaly increasing or monotonicaly decreasing in that interval. .

If I have a vector field (x,y,z) on a one dimensional line (x-axis) and if I have to check its monotonicity between two intervals. Will it be monotonic if:

(1) only one of the components of vector field is monotonic in that interval. OR (2) two of the components of vector field are monotonicaly increasing and the other is monotonicaly decreasing in that interval. OR (3) all the components of vector field are either monotonicaly increasing or monotonicaly decreasing in that interval. .