MATH CALCULATOR
Cross Product Calculator
Calculate the cross product of two vectors easily with our online calculator.
What is the Cross Product Calculator & How does it work?
The cross product is a binary operation on two vectors in three-dimensional space. It results in a vector that is perpendicular to both of the original vectors. The magnitude of the resulting vector is equal to the area of the parallelogram spanned by the two vectors.
The cross product is widely used in physics and engineering to calculate torque, angular momentum, and other vector quantities.
mathbf{a} times mathbf{b} = (a_2b_3 – a_3b_2)mathbf{i} + (a_3b_1 – a_1b_3)mathbf{j} + (a_1b_2 – a_2b_1)mathbf{k}
mathbf{a} = first vector, mathbf{b} = second vector
Parameters
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Frequently Asked Questions
How do I calculate the cross product of two vectors?
To calculate the cross product, multiply the components using the formula: (a2b3 – a3b2)i + (a3b1 – a1b3)j + (a1b2 – a2b1)k.
What is the cross product used for?
The cross product is used in physics and engineering to find a vector perpendicular to two given vectors, often representing torque or magnetic fields.
Can I use this calculator for 2D vectors?
No, this calculator is designed for 3D vectors. The cross product requires two vectors in three-dimensional space.
What does the magnitude of the cross product represent?
The magnitude of the cross product represents the area of the parallelogram formed by the two vectors.
Is the cross product commutative?
No, the cross product is not commutative. The order of the vectors matters: a × b ≠ b × a.
Results are for informational purposes only and do not constitute professional advice.