vector cross product calculator

Using Vector Cross Product Calculator

Given vector A = [2, -1, 3] and vector B = [4, 2, -2], enter the expression this way

[ 2, -1, 3 ] , [ 4, 2, -2 ]

What is Vector Cross Product?

A vector cross product, also known as a vector product, is an operation that takes two vectors and generates a third vector that is perpendicular to both of the original vectors. It is denoted by the symbol "x" or using the cross product notation.

Steps to Solving Vector Cross Product Using Vector Cross Product Calculator

To solve a vector cross product, follow these steps:

1. Identify the two vectors that you want to find the cross product of. Let's call them vector A and vector B.

2. Write down the components of each vector. For example, vector A can be represented as [A₁, A₂, A₃] and vector B can be represented as [B₁, B₂, B₃].

3. Calculate the cross product by following the steps:

• The x-component of the cross product is calculated as: (A₂ B₃) - (A₃ B₂)

• The y-component of the cross product is calculated as: (A₃ B₁) - (A₁ B₃)

• The z-component of the cross product is calculated as: (A₁ B₂) - (A₂ B₁)

4. Combine the components to obtain the resulting vector. The cross product vector will be in the form [x, y, z].

Worked Example of Vector Cross Product

Given vector A = [2, -1, 3] and vector B = [4, 2, -2], the task is to find the cross product of these vectors.

we have:

• The x-component of the cross product = (2 * 2) - (-1 * -2) = 4 - 2 = 2

• The y-component of the cross product = (3 * 4) - (2 * 2) = 12 - 4 = 8

• The z-component of the cross product = (2 * -2) - (4 * -1) = -4 - (-4) = -4 + 4 = 0

Therefore, the cross product of vector A and vector B is [2, 8, 0].