Enter the x, y and z components of both vectors and the calculator returns magnitudes, dot product, cross product and the angle.
The cross product is a vector: (y₁z₂−z₁y₂, z₁x₂−x₁z₂, x₁y₂−y₁x₂), perpendicular to both inputs.
It measures alignment: positive means a similar direction, zero means perpendicular, negative means opposite directions.
θ = arccos((a · b) / (|a| |b|)), using the dot product and both magnitudes.