A particle moves in three dimensional space with a constant acceleration affect the x component of its location? Can the z component of the acceleration affect the y component of the velocity?

As long as the components of the position vector of the particle are independent of each other, the components of velocity vector representing the change in the components of position vector will also be independent of each other.Similarly, the components of acceleration vector would be independent of each other, and any change in z component of the acceleration vector would not bring any change in the x or y component of position and velocity vector of the object.However if one assume a condition in which say the x position of the particle is dependent on the z position. Then any change in z component of velocity vector can be related to changes in x component of position vector. Similarly, any changes in z component of acceleration vector can be accounted for changes in x component of position vector.