That's just a small part of vector calculus.
Vector algebra: dot and cross product and their applications.
Differentiation in multiple dimension: directional derivative, gradient, Hessian, derivative test, multivariable Taylor's polynomial.
Differentiation of vector fields: divergence and curl.
Integration with vectors: flux integral, line integral, antiderivative of vector field, Stokes's theorem and variants of that, formulas for arc length.
Calculus identities involving vector: triple product formula, Jacobi formula, relationship between gradient, curl and divergence.