Vector Dot & Cross Product Calculator

Compute the dot product, cross product (3D), angle, and norms of two vectors A and B.

Input

Enter the components of two vectors A and B to compute the dot product, cross product (3D), angle, and magnitude (norm).

Dimension

Vector A

Component 1

Component 2

Component 3

Vector B

Component 1

Component 2

Component 3

Dot product (a·b)

Angle

12.933154 deg

Angle (radians)

0.225726 rad

Cross product (a×b)

( -3, 6, -3 )

|A| (norm of A)

3.741657

|B| (norm of B)

8.774964

The dot product is the sum of component-wise products: a·b = Σ aᵢbᵢ.
The cross product is computed only for 3D vectors: a×b = (a₂b₃−a₃b₂, a₃b₁−a₁b₃, a₁b₂−a₂b₁).
The norm (magnitude) is the Euclidean length: |a| = √(Σ aᵢ²).
The angle is θ = arccos( a·b / (|a||b|) ), shown in both degrees and radians.
If either vector is the zero vector (norm 0), the angle is undefined and shown as such.

Tell us what you think of this calculator.