freeCodeCamp

2.0 KiB

Raw Blame History

title
Dot Product

Dot Product

A dot product is a way of multiplying two vectors together to get a single number. Dot products are common in physics and linear algebra.

You can write the dot product of two vectors a and b as a · b .

Two vectors must be of the same length to have a dot product.

To find the dot product, multiply the nth element in the first vector by the nth element in the second vector. Do this for all of the elements. Then, find the sum of all those products. This sum is the dot product!

Properties of Dot Products

The dot product of two vectors can also be expressed as a · b = ||a|| * ||b|| * cos(theta). In this formula, ||a|| is the magnitude of vector a, and theta is the angle between the two vectors.

Two orthogonal (a.k.a. perpendicular) vectors will always have a dot product of 0.

Worked Example

For example, say you have the vectors a and b. Let a = (1 2 3 4) and b = (-1 0 1 2).

The dot product would be (1)(-1) + (2)(0) + (3)(1) + (4)(2) = -1 + 0 + 3 + 8 = 12. So in this case, you would say that a · b = 12.

Code Example

Here's an example function in JavaScript. It returns the dot product of two vector arguments:


/**
 * @param {array} a - A vector/array of numbers
 * @param {array} b - A vector/array of numbers with the same length as a
 * @returns {number} - The dot product of a and b
 */
function dotProduct(a, b) {
  // Check if the lengths are the same - if not, there can't be a dot product
  if (a.length !== b.length) {
    throw "vector lengths must be equal";
  }

  // Create a variable to store the sum as we calculate it
  let product = 0;

  // Loop through the vectors, calculate products, and add them to the total
  for (let i = 0; i < a.length; i++) {
    // You may want to ensure that a[i] and b[i] are both finite numbers
    product += a[i] * b[i];
  }

  return product;
}

More Information:

Vectors

2.0 KiB Raw Blame History