Vector Angle

The angle between two vectors can be computed using the dot product. If and are two vectors, their angle is given by:

In JavaScript, we can implement a simple angle function to compute the angle between two vectors.

code.js
1function angle(u, v) {
2  const dotProd = dotProduct(u, v);
3  const magU = magnitude(u);
4  const magV = magnitude(v);
5  if (magU === 0 || magV === 0) {
6    throw new Error("Cannot compute angle with zero magnitude vector.");
7  }
8  
9  const cosTheta = dotProd / (magU * magV);
10  
11  // Ensure the value is within the valid range for acos
12  if (cosTheta < -1 || cosTheta > 1) {
13    throw new Error("Numerical error: cosine value out of range.");
14  }
15  
16  return Math.acos(cosTheta);
17}
18
19function magnitude(v) {
20  return Math.sqrt(v.reduce((sum, e) => sum + e ** 2, 0));
21}
22
23function dotProduct(u, v) {
24  return u.reduce((sum, value, index) => sum + value * v[index], 0);
25}
26
27const u = [1, 2, 3];
28const v = [4, 5, 6];
29
30const theta = angle(u, v);
31console.log(theta);