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

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

What is the Answer?

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?

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

Example calculations for the Cross Product Calculator

Cross Product Calculator Video

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