const square = (n) => {
  return n * n;
};

const magnitude = (v = [], i = 0, n = 0) => {
  if (!v.length) return false;
  n += square(v[i]);
  if (i === v.length-1) {
    return Math.sqrt(n);
  } else {
    return magnitude(v, i+1, n);
  }
};

const normalisation = (v = []) => {
  if (!v.length) return false;
  let m = 1 / magnitude(v);
  for ( var i = 0; i < v.length; i++ ) {
    v[i] = m * v[i];
  }
  return v;
};