How to Use the 2D & 3D Vector Math (Dot & Cross Product)
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Select dimension: 2D (x, y) or 3D (x, y, z).
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Enter coordinates for Vector A and Vector B.
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The calculator computes: Magnitudes $|A|$ and $|B|$, Unit Vectors, Dot Product ($A \cdot B$), and 3D Cross Product ($A \times B$).
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View the angle $\theta$ between the vectors in both degrees and radians.
Practical Example & Use Case
Common Real-World Scenario
Finding the angle between vectors $[1, 0, 0]$ and $[0, 1, 0]$ is exactly $90.0^\circ$ with a dot product of $0$ (orthogonal vectors).
Technical Notes & Limitations
Browser Engine Architecture
Cross product is mathematically defined exclusively for 3-dimensional Euclidean vectors (or 7-dimensional).
Frequently Asked Questions
What does a dot product of zero signify?
A dot product of zero indicates that the two non-zero vectors are perpendicular (orthogonal) to each other ($cos 90^circ = 0$).