To calculate the product of two vectors in a programming language, we can use the dot product formula. The dot product of two vectors a and b is given by:

a · b = a1*b1 + a2*b2 + ... + an*bn
Here's a brief snippet in JavaScript using the @thi.ng/vectors library:

import { vector } from '@thi.ng/vectors';

const a = vector([1, 2, 3]);
const b = vector([4, 5, 6]);

const dotProduct = vector.dot(a, b);
console.log(dotProduct); // Output: 32

Note that this library provides optimized implementations for various vector operations, including the dot product.