isotropic quot scheme is a projective scheme that compactifies the moduli space of maps (of a given degree) from a smooth projective algebraic curve to an isotropic grassmannian. isotropic quot schemes are often not smooth, but we construct a virtual fundamental class which makes it 'virtually' smooth. we use this to understand intersection theory of this space and find a vafa-intriligator type formula for the intersection of certain cohomology classes.