Cross Product Calculator

Publish date: 2024-06-14

Given the following two vectors in R3:
calculate the cross product X × Y
X = 2i + j + 2k
Y = 3i - j - 3k

Write the coefficients as a matrix

i	j	k
x1	x2	x3
y1	y2	y3

i	j	k
2	1	2
3	-1	-3

Evaluate Cross Product Formula

X × Y = (x2y3 - x3y2)i + (x3y1 - x1y3)j + (x1y2 - x2y1)k
X × Y = (1 x -3 - 2 x -1)i + (2 x 3 - 2 x -3)j + (2 x -1 - 1 x 3)k
X × Y = (-3 - -2)i + (6 - -6)j + (-2 - 3)k
X × Y = - i + 12j - 5k

Parallel Check:

Since X × Y <> 0:
X and Y are not parallel

X × Y = - i + 12j - 5k
Since X × Y <> 0:
X and Y are not parallel

What is the Answer?

X × Y = - i + 12j - 5k
Since X × Y <> 0:
X and Y are not parallel

How does the Cross Product Calculator work?

Free Cross Product Calculator - Given two vectors A and B in R3, this calculates the cross product A × B as well as determine if the two vectors are parallel
This calculator has 6 inputs.

What 1 formula is used for the Cross Product Calculator?

X × Y = (x2y3 - x3y2)i + (x3y1x1y3)j + (x12x2y1)k

For more math formulas, check out our Formula Dossier

What 4 concepts are covered in the Cross Product Calculator?

cross producta binary operation on two vectors in a three-dimensional oriented Euclidean vector spaceformulaa fact or a rule written with mathematical symbols. A concise way of expressing information symbolically.parallelvectordirected line segment

Example calculations for the Cross Product Calculator