---
title: Vector dot product
id: 594810f028c0303b75339ad3
challengeType: 5
---

## Description
<section id='description'>
<p>
A vector is defined as having three dimensions as being represented by an ordered collection of three numbers: &nbsp; (X, Y, Z).
</p>
<p>
Task:

    Write a function that takes any numbers of vectors (arrays) as input and computes their dot product.

Your function should return <code>null</code> on
invalid inputs (ie vectors of different lengths).
</p>
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: dotProduct must be a function
    testString: 'assert.equal(typeof dotProduct, "function", "dotProduct must be a function");'
  - text: dotProduct() must return null
    testString: 'assert.equal(dotProduct(), null, "dotProduct() must return null");'
  - text: 'dotProduct([[1], [1]]) must return 1.'
    testString: 'assert.equal(dotProduct([1], [1]), 1, "dotProduct([[1], [1]]) must return 1.");'
  - text: 'dotProduct([[1], [1, 2]]) must return null.'
    testString: 'assert.equal(dotProduct([1], [1, 2]), null, "dotProduct([[1], [1, 2]]) must return null.");'
  - text: 'dotProduct([1, 3, -5], [4, -2, -1]) must return 3.'
    testString: 'assert.equal(dotProduct([1, 3, -5], [4, -2, -1]), 3, "dotProduct([1, 3, -5], [4, -2, -1]) must return 3.");'
  - text: <code>dotProduct(...nVectors)</code> should return 156000
    testString: 'assert.equal(dotProduct([ 0, 1, 2, 3, 4 ], [ 0, 2, 4, 6, 8 ], [ 0, 3, 6, 9, 12 ], [ 0, 4, 8, 12, 16 ], [ 0, 5, 10, 15, 20 ]), 156000, "<code>dotProduct(...nVectors)</code> should return 156000");'

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function dotProduct() {
    // Good luck!
}
```

</div>



</section>

## Solution
<section id='solution'>


```js
function dotProduct(...vectors) {
  if (!vectors || !vectors.length) {
    return null;
  }
  if (!vectors[0] || !vectors[0].length) {
    return null;
  }
  const vectorLen = vectors[0].length;
  const numVectors = vectors.length;

  // If all vectors not same length, return null
  for (let i = 0; i < numVectors; i++) {
    if (vectors[i].length !== vectorLen) {
      return null;  // return undefined
    }
  }

  let prod = 0;
  let sum = 0;
  let j = vectorLen;
  let i = numVectors;
  // Sum terms
  while (j--) {
    i = numVectors;
    prod = 1;

    while (i--) {
      prod *= vectors[i][j];
    }
    sum += prod;
  }
  return sum;
}

```

</section>