Online 2D & 3D Vector Calculator
Perform vector operations in two and three-dimensional Cartesian space. Instantly calculate magnitude, addition, subtraction, dot product, cross product, and angle between vectors.
Vector A
Vector B
How to use
- Select coordinate space dimensionality (2D planar or 3D spatial).
- Input vector components for vectors A and B.
- Select specific vector operation or view comprehensive multi-operation summary.
Key Vector Operations
Vector Magnitude: |A| = √(x² + y² + z²).
Dot (Scalar) Product: A · B = x1*x2 + y1*y2 + z1*z2.
Cross Product (3D): yields an orthogonal normal vector perpendicular to both vectors.
Angle between Vectors: cos(α) = (A · B) / (|A| * |B|).
Calculation Methodology
Calculations use standard Cartesian coordinates and theorems from analytic geometry and linear algebra.
Frequently Asked Questions
What is the difference between dot and cross products?
The dot product produces a scalar number, while the cross product outputs a vector perpendicular to both initial vectors.
How is the angle between two vectors calculated?
By dividing their dot product by the product of their respective magnitudes (arccosine).
Can you add a 2D vector to a 3D vector?
No, vector algebra requires vectors to have matching dimensional space.
What does a dot product of zero signify?
A dot product of zero for non-zero vectors indicates that they are perpendicular (orthogonal) at a 90° angle.
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