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In a camera model, in order to find the camera calibration, how do we find the the parameters from the vector a in the equation $Ca=0$? I know that the camera matrix to convert a world point to image point is $K[R|T]$ which is $3\times4$ matrix. If we know $6$ correspondences of world point to image point, we can find the vector $a$. The equation $Ca=0$ was derived from $x=K[R|T]X$ where $x$ is image point and $X$ is world point. I know that we have to take the nullspace of $C$ which can be done using SVD but what then? How we will we know the values of vector $a$? Note: a vector contains all the values in $K[R|T]$ matrix.

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You need to convert $a$ back into a 3x4 matrix, then do intrinsic/extrinsic decomposition. I've written a tutorial on this at my blog.

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