About This Calculator
This Cross Product Calculator quickly finds the cross product of two 3D vectors. The result is a vector perpendicular to both inputs, widely used in physics, engineering, and geometry for direction and area calculations.
How It Works
- Enter each component of Vector A and Vector B separately in the input fields.
- Click "Calculate" to see the cross product result.
- The calculator shows each component of the result and detailed step-by-step calculations using vector notation.
\vec{A} \times \vec{B} = \begin{vmatrix}\hat{i} & \hat{j} & \hat{k} \\a_1 & a_2 & a_3 \\b_1 & b_2 & b_3 \\\end{vmatrix}
x = a₂ × b₃ − a₃ × b₂
y = a₃ × b₁ − a₁ × b₃
z = a₁ × b₂ − a₂ × b₁
y = a₃ × b₁ − a₁ × b₃
z = a₁ × b₂ − a₂ × b₁
Frequently Asked Questions
What is the cross product?
The cross product of two 3D vectors gives a vector that is perpendicular to both inputs. Its direction follows the right-hand rule.
Can I calculate cross products for more than 3 dimensions?
No, the standard cross product only applies to 3D vectors.
What happens if the vectors are parallel?
If the vectors are parallel or one is a zero vector, the cross product result is the zero vector.
How should I enter the vector components?
Enter each component in the corresponding input field. All six values must be valid numbers.