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Interference of Beams with Different Polarizations

I have read in many places that orthogonally polarized light beams do not interfere. However, I also know that orthogonal vectors, such as force, do affect each other and give a resulting force. So, since amplitude is a vector, shouldn't the amplitudes of orthogonally polarized beams add up in some way and produce a resulting amplitude? If so, could this be called interference?