# Cross Product of Vectors and Determinants

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Examples, solutions, videos, worksheets, games, and activities to help Algebra students learn how to find the cross product of vectors using determinants.

The Cross Product of Vectors
In Calculus we often use the cross product of vectors to find orthogonal vectors and the area of parallelograms in three dimensions. The cross product of vectors is found by identifying the 3x3 determinants, however we substitute one of the rows with symbols that represent unit vectors. Finding 3x3 determinants can be made easier if we understand how to simplify determinants.

This video explains how to determine the cross product to two vectors, how to verify two vectors are orthogonal, and how to determine the angle between two vectors.

The Cross Product
This video gives the formula for the cross product of two vectors, discuss geometrically what the cross product is, and do an example of finding the cross product.

Cross Product Area
Finding the area of a parallelogram in two dimensions involves the area determinant of a 2x2 matrix, but if we’re given a parallelogram in three dimensions we can use the cross product area. The cross product area is a technique often used in vector calculus. The cross product is found using methods of 3x3 determinants, and these methods are necessary for finding the cross product area.

Area of Triangle Formed by Two Vectors using Cross Product.
Here we find the area of a triangle formed by two vectors by finding the magnitude of the cross product.

Finding the Area of a Triangle using Cross Product

Area of a Parallelogram using Cross Product

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