 # (8i + -1j + 3k) x (5i + 1j + -9k)

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 - j + 3k
Y = 5i + j - 9k

## Write the coefficients as a matrix

 i j k x1 x2 x3 y1 y2 y3
→
 i j k 8 -1 3 5 1 -9

## Evaluate Cross Product Formula

X × Y = (x2y3 - x3y2)i + (x3y1 - x1y3)j + (x1y2 - x2y1)k
X × Y = (-1 x -9 - 3 x 1)i + (3 x 5 - 8 x -9)j + (8 x 1 - -1 x 5)k
X × Y = (9 - 3)i + (15 - -72)j + (8 - -5)k
X × Y = 6i + 87j + 13k

## Parallel Check:

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

X × Y = 6i + 87j + 13k
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