# Cross Products

The cross product is an essential concept in vector mathematics, especially in physics and engineering. It involves the multiplication of two vectors to produce a new vector that is perpendicular to both input vectors. The cross product is typically used to calculate the area of a parallelogram, the torque applied to an object, and the orientation of magnetic and electric fields.

## How to calculate the cross product

To calculate the cross product of two vectors A and B in three-dimensional space, we use the following formula:

_{y}* B

_{z}- A

_{z}* B

_{y}) i - (A

_{x}* B

_{z}- A

_{z}* B

_{x}) j + (A

_{x}* B

_{y}- A

_{y}* B

_{x}) k

where A

_{x}, A

_{y}, and A

_{z}are the components of vector A, and B

_{x}, B

_{y}, and B

_{z}are the components of vector B. The resulting cross product is a new vector with components i, j, and k.

## Cross product properties

The cross product is anticommutative, meaning:

The cross product is distributive:

The scalar multiplication property:

## Cross product example

Given two vectors

= (-3) i - (-6) j + (-3) k

=

-3, 6, -3>

In this example, the cross product of vectors A and B is the vector

-3, 6, -3>

## Topics related to the Cross Products

Solving Systems of Linear Equations

## Flashcards covering the Cross Products

## Practice tests covering the Cross Products

Multivariable Calculus Practice Tests

## Get more help with the cross product

A tutor can equip your student with plenty of math tricks, including working with vectors and much more. Varsity Tutors carefully vets each tutor, ensuring that your student always works alongside someone who truly understands these concepts. If your student isn''t clear about cross-multiplying and other important concepts covered in class, they can ask as many questions as they like during these 1-on-1 sessions. Reach out today, and Varsity Tutors will match your student with a suitable tutor.

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