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I am quite confused by the topic "Update a projection matrix from rVec and tVec" but if you are looking for a solution to obtain projection matrix from camera calibration with present intrinsic and extrinsic parameters you can do the following:

cv::Mat computeProjMat(cv::Mat camMat, vector<cv::Mat> rotVec, vector<cv::Mat> transVec)
    cv::Mat rotMat(3, 3, CV_64F), rotTransMat(3, 4, CV_64F); //Init.
    //Convert rotation vector into rotation matrix 
    cv::Rodrigues(rotVec[0], rotMat);
    //Append translation vector to rotation matrix
    cv::hconcat(rotMat, transVec[0], rotTransMat);
    //Compute projection matrix by multiplying intrinsic parameter 
    //matrix (A) with 3 x 4 rotation and translation pose matrix (RT).
    //Formula: Projection Matrix = A * RT;
    return (camMat * rotTransMat);