projecting a 3D vector field onto a 2D plane

Hi,

I have a vector field (k= k1, k2, k3), these are spherical coordinates beasically, (). I have values as following:

theta = pi/2; and phi as a matrix here. ( also what if I have a phi as a function of x)

I want to plot k on 2D plane with following properties:

1. k3 should give a colourmap for the plane, k3 increases monotonically from −1 to +1 as I move along Y.
2. (k1, k2) has a constant direction should do a quiver plot on the plane. Along lines parallel to the x-axis, k3 is constant and hence the vector (k1, k2) has constant magnitude, but rotates through one revolution, being asymptotically vertical at both ends of the line.

what should be the idea or lines of code? plot shall be something like