The dot product returns a scalar that measures alignment, while the cross product returns a vector perpendicular to two three-dimensional vectors. Learn the formulas, geometric meaning, right-hand rule, projections, work, area, plane normals, torque, flux, scalar triple products, Lagrange’s identity, and complete worked examples.
The Divergence Theorem converts outward flux through a closed surface into a triple integral of divergence over the enclosed solid. Learn the theorem’s conditions, flux and divergence meanings, method-selection rules, singularity warnings, and a complete sphere example with exact verification.
Green’s Theorem turns a boundary line integral into an interior double integral. In this Woody Calculus visual lesson, learn how Green’s Theorem connects circulation, curl, flux, area, line integrals, double integrals, Stokes’ Theorem, and the Divergence Theorem in Calculus 3.