eigen/doc/examples/tut_arithmetic_dot_cross.cpp

#include <iostream>
#include <Eigen/Dense>

int main() {
  Eigen::Vector3d v(1, 2, 3);
  Eigen::Vector3d w(0, 1, 2);

  std::cout << "Dot product: " << v.dot(w) << std::endl;
  double dp = v.adjoint() * w;  // automatic conversion of the inner product to a scalar
  std::cout << "Dot product via a matrix product: " << dp << std::endl;

  std::cout << "Cross product:\n" << v.cross(w) << std::endl;
  Eigen::Vector2d v2(1, 2);
  Eigen::Vector2d w2(0, 1);
  double cp = v2.cross(w2);  // returning a scalar between size-2 vectors
  std::cout << "Cross product for 2D vectors: " << cp << std::endl;
}