# Cross Product Calculator

Cross Product Calculator calculates the cross product of the given two vectors. The cross product of the two arrows is defined as the third arrow that is perpendicular to the two original arrows.

## What is Cross Product Calculator?

Cross Product Calculator is an online tool that helps to calculate the cross product of the given two vectors. It helps you to calculate the cross product in a few seconds. To use this cross product calculator, enter the values up to two digits only.

## How to Use Cross Product Calculator?

Please follow the steps below to find the cross product using an online cross product calculator:

**Step 1:**Go to Cuemath’s online cross product calculator**Step 2:**Enter the coefficients of two vectors in the given input boxes of the cross product calculator.**Step 3:**Click on the**"Calculate"**button to calculate the cross product.**Step 4:**Click on the**"Reset"**button to clear the fields and enter the different values.

## How Cross Product Calculator Works?

**Vectors** are quantities with both magnitude and direction. Vectors help to simultaneously represent different quantities in the same expression.

The standard form of representation of a vector is:

a = a_{1}i^ + a_{2}j^ + a_{3}k^

b = b_{1}i^ + b_{2}j^ + b_{3}k^

Where a_{1}, b_{1}, c_{1,} and a2, b_{2}, c_{2 }are numeric values and i^, j^, k^ are the unit vectors along the x-axis, y-axis, and z-axis respectively.

When two vectors are multiplied with each other and the product is also a vector quantity, then the resultant vector is called the **cross product** or the vector product. Cross product is represented by a × b. The cross product of two vectors is given by:

Cross product(a × b) = i(a_{2}b_{3 }− a_{3}b_{2}) − j(a_{1}b_{3 }− a_{3}b_{1}) + k(a_{1}b_{2 }− a_{2}b_{1})

**Solved Example on Cross Product:**

Find the cross product of two vectors a = 4i + 2j – 5k and b = 3i – 2j + k and verify it using cross product calculator?

**Solution:**

Given a = 4i + 2j – 5k and b = 3i – 2j + k

a × b = i(a_{2}b_{3 }− a_{3}b_{2}) − j(a_{1}b_{3 }− a_{3}b_{1}) + k(a_{1}b_{2 }− a_{2}b_{1})

= i((2 × 1) - (-5) × (-2)) - j((4 × 1 - (5) × (3)) + k((4) × (-2) - (2 × 3))

= i(2 - 10) - j(4 + 15) + k(-8 - 6)

= -8i - 19j - 14k

Therefore, the cross product of two vectors is -8i - 19j - 14k

Similarly, you can use the cross product calculator to find the cross product of two vectors for the following:

- a = 4i + 2j - 5k and b = -1i + 4j - 3k
- a = -2i - 5k and b = -7i + j + k