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

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

What is the Answer?

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?

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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