Eigen remove for in plane line(s) intersection method - c++

Question

I'm trying to do a plane line(s) intersection method using Eigen. The code works, but I want to remove the for loop (used to process each point). The goal is to make this method run as fast as possible.
Input: planeNormal, planePoint, linesP0 (3xN), linesp1 (3xN)
Output: intersetcionsPoints (3xN)
Number of points is N
Complete code:
void PlaneLineIntersect(const Vector3f &planeNormal, const Vector3f &planeP0, const Matrix3Xf &linesP0, const Matrix3Xf &linesP1, Matrix3Xf &I, float &t)
{
Matrix3Xf p0l0(linesP0.rows(), linesP0.cols());
// ################################
// ## HOW TO REMOVE THIS FOR (colwise?) ##
for (int i = 0; i < linesP0.cols(); i++)
{
float denom = planeNormal.dot(linesP1.col(i) - linesP0.col(i));
if (denom > 1e-6 || denom < -1e-6) // há uma interseção
{
Vector3f p0l0 = planeP0 - linesP0.col(i);
t = p0l0.dot(planeNormal) / denom;
p0l0 = (t * (linesP1.col(i) - linesP0.col(i))) + linesP0.col(i);
I.col(i) = p0l0;
}
}
}
int main(cli::array<System::String ^> ^args)
{
int n = 1000;
Eigen::Vector3f planeNormal = Eigen::Vector3f(0, 0, -1);
Eigen::Vector3f planeP0 = Eigen::Vector3f(0, 0, 7);
Eigen::Matrix3Xf linesP0 = Matrix3Xf::Random(3, n);
Eigen::Matrix3Xf linesP1 = Matrix3Xf::Random(3, n);
Eigen::Matrix3Xf I = Matrix3Xf::Zero(3, n);
float t;
high_resolution_clock::time_point t1 = high_resolution_clock::now();
#pragma omp parallel for
for (int i = 0; i < 100; i++)
PlaneLineIntersect(planeNormal, planeP0, linesP0, linesP1, I, t);
high_resolution_clock::time_point t2 = high_resolution_clock::now();
double duration = (double) (duration_cast<microseconds>(t2 - t1).count());
cout << "\nTempo total = " << duration / 1000 << " ms" << endl;
cout << "\nTempo / ponto = " << duration / (n * 100) << " us\n" << endl;
system("pause");
return 0;
}