I want to draw the world coordinates vector in left bottom corner of the viewport using opengl. Is it possible to multiply the vectors (1, 0, 0) (0, 1, 0) (0, 0, 1) vectors in view space by inverse of the view matrix and then project the result vectors on the screen?
Just set the 4th column and row of the modelview matrix to [0, 0, 0, 1], orthonormalize the upper left 3×3 submatrix and draw your base vector tripod with the glViewport set to the corner of the window where you want it to be.
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