vector

vector.js

var V = {
  init: function(x, y, z) {
    return { x: x, y: y, z: z };
  },
  
  add: function(v1, v2) {
    return {
      x: v1.x + v2.x,
      y: v1.y + v2.y,
      z: v1.z + v2.z        
    };
  },

  joining: function(v1, v2) {
    return V.add(v2, V.scale(v1, -1));
  },
  
  dot: function(v1, v2) {
    return v1.x*v2.x + v1.y*v2.y + v1.z*v2.z;
  },
      
  product: function(v1, v2) {
    return {
      x: v1.y * v2.z - v1.z * v2.y,
      y: v1.z * v2.x - v1.x * v2.z,
      z: v1.x * v2.y - v1.y * v2.x
    };
  },

  areEqual: function(v1, v2) {
    return (v1.x == v2.x) && (v1.y == v2.y) && (v1.z == v2.z);
  },

  scale: function(v, k) {
    return {
      x: v.x * k,
      y: v.y * k,
      z: v.z * k
    };
  },

  isLinearMultiple: function(v1, v2) {
    if (V.isZero(v1) && V.isZero(v2)) { return true }
    else if (V.isZero(v1)) { return false }
    else {
      if (!v1.x == 0) { return V.areEqual(v1, V.scale(v2, (v1.x / v2.x))) }
      if (!v1.y == 0) { return V.areEqual(v1, V.scale(v2, (v1.y / v2.y))) }
      if (!v1.z == 0) { return V.areEqual(v1, V.scale(v2, (v1.z / v2.z))) }           
    }
  },
  
  isZero: function(v) {
    return V.areEqual(v, V.init(0, 0, 0));
  },

  normalize: function(v) {
    var length = V.magnitude(v);
    return {
      x: v.x / length,
      y: v.y / length, 
      z: v.z / length       
    };
  },

  magnitude: function(v) {
    return Math.sqrt(v.x*v.x + v.y*v.y + v.z*v.z);
  }
};

/* 
The picture:
                                           
                                                [P]
                       [C]                       |
                      /                          ^ 
                   /\                            p
                  t                              e
                s                                r
              e                                  p
            d                                    |  
          /                                      |
        /                                        |
     [A]---- s o u r c e > ---------------------[B]

Where (A->C = dest), (A->B = source), (B=>P = perp)
*/

// Position vectors:
var a = V.init(0, 0, 0),
    b = V.init(1, 2, 0),
    c = V.init(1, 1, 1);
    
// Direction vectors:    
var source = V.joining(a, b),
    dest   = V.joining(a, c);
         
// Othogonal component of source vector, with respect to destination vector.
var perp = V.normalize(V.product(V.product(source, dest), source));
if (V.magnitude(V.joining(perp, c)) > V.magnitude(V.joining(b, c))) { perp = V.scale(perp, -1) };

console.log("x: " + perp.x + " y: " + perp.y + " z: " + perp.z)