3d vector interpolation: 2 phasors of known amplitude

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castwerks

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I have two phasors of known amplitude and phase (A1, P1 and A2, P2) (shown in red) rotating at the same speed in the Y-Z plane at different locations along the X axis. How can I calculate the amplitude and phase of a third phasor, determined by a (blue) line connecting the two orginal phasors, also rotating in the Y-Z plane located at a known Xo postion (shown in green)?



Thanks for the help.
 
Re: 3d vector interpolation

castwerks said:
I have two phasors of known amplitude and phase (A1, P1 and A2, P2) (shown in red) rotating at the same speed in the Y-Z plane at different locations along the X axis. How can I calculate the amplitude and phase of a third phasor, determined by a (blue) line connecting the two orginal phasors, also rotating in the Y-Z plane located at a known Xo postion (shown in green)?



Thanks for the help.
Click to expand...

Please show your work, indicating exactly where you are stuck - so that we know where to begin to help you.
 
my first thought on how to go about it would be to convert each phasor to cartesian coordinates (using A*sin(theta), A*cos(theta)).

This would give me (x1,y1,z1) and (x2,y2,z2). From there I would calculate the equation of the line passing through the two points.

Next I would find the intersection point of the YZ plane (located at X0) and the calculated line form the step above.

Finally I would convert my intersection point (x3,y3,z3) back in to phasor form by finding the amplitude (y^2+z^2)^.5 and phase (atan(z/y)).
 
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