Cross product calculator calculates the cross product of two vectors ** a** and

**in three-dimensional space**

*b***Enter**

*.**i, j,*and

*k*for both vectors to get the resultant vector

*c.**c = a × b*

This vector cross product calculator shows step by steps vector multiplication.

## What is cross product?

Cross product is a multiplication of two vectors in three-dimensional space. It is denoted by the symbol ** ‘×’**. Cross product of two vectors

**and**

*a***is a vector that is perpendicular to both**

*b***and**

*a*

*b.*Note: Read ** a × b **as

**cross**

*a*

*b.*Image credit: “Cross Products” by Khan Academy.

## Cross product formula

Below equation is used to find the cross product of two vectors.

**a × b** = |**a**| |**b**| sin(θ) **n**

In this equation:

|**a**| is length of vector **a**

|**b**| is length of vector **b**

**θ** is the angle between **a** and **b**

**n** is the unit vector perpendicular to **a** and **b.**

We can also calculate cross product by using the coordinate points of both vectors.

*(a _{i} a_{j} a_{k}) × (b_{i} b_{j} b_{k}) = (a_{j} × b_{k} - a_{k} × b_{j} a_{k} × b_{i} - a_{i} × b_{k} a_{i} b_{j} - a_{j} × b_{i})*

Where

** i, j,** and

**represents**

*k***and**

*x, y,***coordinates on Cartesian plane.**

*z*

**References:**

Formula of Cross Product. Retrieved from MathisFun.