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.