 # (8i + -2j + 13k) x (3i + 5j + -1k)

i  j  k

## Enter y1i + y2j + y3k

i  i  k

Given the following two vectors in R3:
calculate the cross product X × Y
X = 8i - 2j + 13k
Y = 3i + 5j - k

## Write the coefficients as a matrix

 i j k x1 x2 x3 y1 y2 y3
→
 i j k 8 -2 13 3 5 -1

## Evaluate Cross Product Formula

X × Y = (x2y3 - x3y2)i + (x3y1 - x1y3)j + (x1y2 - x2y1)k
X × Y = (-2 x -1 - 13 x 5)i + (13 x 3 - 8 x -1)j + (8 x 5 - -2 x 3)k
X × Y = (2 - 65)i + (39 - -8)j + (40 - -6)k
X × Y = - 63i + 47j + 46k

## Parallel Check:

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

X × Y = - 63i + 47j + 46k
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?

1. 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 product
a binary operation on two vectors in a three-dimensional oriented Euclidean vector space
formula
a fact or a rule written with mathematical symbols. A concise way of expressing information symbolically.
parallel
vector
directed line segment