Algebra

Cross Product Calculator

Easily calculate the cross product of two 3D vectors online. Input vector components and get instant results with visual representation and formula. Free and user-friendly!

Vector a

Vector b

Result:

Result will be displayed here after calculation.

Understanding Cross Product

The cross product, also known as the vector product, is a binary operation on two vectors in three-dimensional space. It results in a vector that is perpendicular to both of the input vectors.

Formula: For two vectors $$\vec{a} = (a_x, a_y, a_z)$$ and $$\vec{b} = (b_x, b_y, b_z)$$, their cross product $$\vec{a} \times \vec{b}$$ is calculated as:

$$ \vec{a} \times \vec{b} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ a_x & a_y & a_z \\ b_x & b_y & b_z \end{vmatrix} = (a_y b_z - a_z b_y)\mathbf{i} - (a_x b_z - a_z b_x)\mathbf{j} + (a_x b_y - a_y b_x)\mathbf{k} $$

Applications: The cross product has numerous applications in physics and engineering, including calculating torque, angular momentum, and magnetic forces. It is also used in computer graphics for surface normals and lighting calculations.

Learn more about cross product on Wikipedia.

Frequently Asked Questions

What is the Cross Product Calculator?
The Cross Product Calculator is an online Algebra calculator. You enter your values, and it returns the answer with the steps shown so you can follow along.
How accurate is the Cross Product Calculator?
The solver uses a math engine that avoids the floating-point rounding errors you get from most hardware calculators. For typical homework and professional calculations, the results will match what you would get by hand.
Can I use the Cross Product Calculator for professional Algebra projects?
Yes. The math behind it is standard Algebra, so the results are reliable for professional use. That said, always double-check that your inputs are in the right format before relying on the output.
Why use the Cross Product Calculator instead of calculating by hand?
Manual calculation is slow and error-prone, especially with multiple steps. This tool does the arithmetic for you and shows each step, so you can catch mistakes before they carry forward.
How do I format my inputs for the Cross Product Calculator?
Type your numbers into the input fields. Leave out units and symbols unless a field specifically asks for them. The solver handles the rest.

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