 # (6i + -3j + 6k) x (8i + 2j + -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 = 6i - 3j + 6k
Y = 8i + 2j - 9k

## Write the coefficients as a matrix

 i j k x1 x2 x3 y1 y2 y3
→
 i j k 6 -3 6 8 2 -9

## Evaluate Cross Product Formula

X × Y = (x2y3 - x3y2)i + (x3y1 - x1y3)j + (x1y2 - x2y1)k
X × Y = (-3 x -9 - 6 x 2)i + (6 x 8 - 6 x -9)j + (6 x 2 - -3 x 8)k
X × Y = (27 - 12)i + (48 - -54)j + (12 - -24)k
X × Y = 15i + 102j + 36k

## Parallel Check:

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

X × Y = 15i + 102j + 36k
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