// How do you compute the cross product of two 3D vectors? Write the formula explicitly.
#include <iostream>
#include <array>
// ------------------------------------------------------------
// Compute the cross product of two 3D vectors a × b.
// The cross product produces a new vector that is perpendicular
// to both a and b.
//
// Explicit formula for a = (ax, ay, az) and b = (bx, by, bz):
//
// a × b = ( ay*bz - az*by,
// az*bx - ax*bz,
// ax*by - ay*bx )
//
// This matches the determinant expansion:
//
// | i j k |
// | ax ay az |
// | bx by bz |
// ------------------------------------------------------------
std::array<double, 3> cross(const std::array<double, 3>& a,
const std::array<double, 3>& b) {
return {
a[1]*b[2] - a[2]*b[1], // x-component
a[2]*b[0] - a[0]*b[2], // y-component
a[0]*b[1] - a[1]*b[0] // z-component
};
}
int main() {
// 3D vectors // A 3D vector has exactly three components:
std::array<double, 3> a = {1, 0, 2};
std::array<double, 3> b = {3, 1, 0};
// Compute cross product
auto c = cross(a, b);
std::cout << "Cross product: ["
<< c[0] << ", " << c[1] << ", " << c[2] << "]\n";
}
/*
run:
Cross product: [-2, 6, 1]
*/
