Ground plane estimation from a single image (was: confusion about homography and calibration camera parameters)
Yes it is possible to compute the extrinsics given the intrisics, some points in 3D and their projections in the image.  If all your 3D points are in the same plane, then the math for computing the extrinsics is explained in the paper by Zhengyou Zhang, which is the basis for the camera calibration code in OpenCV.

If your 3D points are not co-planar, then you need to use a different algorithm that is described in Hartley and Zisserman.