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If i have

F(x,y,z) = zj; where j is the vector, j hat.

Would that be all vectors are going to be pointing up if you assume z is up, and are in the y plane?

If the coordinate sytem is, z is up, y is to the right, and x is pointing at you.

If i had F(x,y,z) = yj; the answer is, No vectors emanate from the xz plane since y = 0 there. In each plane y = b, all the vectors are identical.