Vector Cross Product Calculator

Cross Product Calculator

Vector A
Vector B

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Cross Product Calculator

The Cross Product Calculator finds the vector perpendicular to two three-dimensional vectors. The result is useful in vector mathematics, physics, geometry, and engineering calculations.

How to use this calculator

Enter the x, y, and z components for both vectors. Check that each vector has three components and that the values are entered in the intended order.

Formula

a Γ— b = (aβ‚‚bβ‚ƒβˆ’a₃bβ‚‚, a₃bβ‚βˆ’a₁b₃, a₁bβ‚‚βˆ’aβ‚‚b₁).

Quick check

If the two input vectors are parallel, their cross product should be the zero vector. The result should also be perpendicular to both original vectors.

Frequently Asked Questions FAQ

What does the Vector Cross Product Calculator calculate?
It calculates the vector perpendicular to two input vectors in three-dimensional space.
Which vectors can be used?
The standard cross product uses two 3D vectors, a = (a₁,aβ‚‚,a₃) and b = (b₁,bβ‚‚,b₃).
What is the cross product formula?
a Γ— b = (aβ‚‚b₃ βˆ’ a₃bβ‚‚, a₃b₁ βˆ’ a₁b₃, a₁bβ‚‚ βˆ’ aβ‚‚b₁).
What does the direction of the result mean?
The result is perpendicular to both input vectors, with its orientation determined by the right-hand rule.
How can I check the magnitude?
The magnitude should satisfy absolute valuea Γ— babsolute value = absolute valueaabsolute valueabsolute valuebabsolute valuesinΞΈ, where ΞΈ is the angle between the two vectors.
What is a common cross-product mistake?
Swapping the vectors changes the sign: b Γ— a = βˆ’(a Γ— b). Also check the middle component carefully because its sign is easy to reverse.

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