Vector Calculator

About the Vector Calculator

The vector calculator is a professional online math tool designed for 2D and 3D vector operations. It provides 8 core vector operations (vector addition, vector subtraction, dot product, cross product, vector magnitude, angle between vectors, unit vector, and vector projection) to meet the needs of students, teachers, and engineers in math, physics, and engineering calculations.

How to Use the Vector Calculator?

1. Choose the dimension: supports 2D and 3D calculations.
2. Enter the vector values: click the "Example" button to see how to enter them.
3. Select the operation type: includes 8 types of calculations.
4. View the results: see the result and steps for each operation.

Vector Formulas

• 1. Vector addition: a + b = (a₁ + b₁, a₂ + b₂, a₃ + b₃)
• 2. Vector subtraction: a - b = (a₁ - b₁, a₂ - b₂, a₃ - b₃)
• 3. Dot product (inner product): a · b = a₁b₁ + a₂b₂ + a₃b₃ = |a| |b| cosθ
• 4. Cross product (outer product): a × b = (a₂b₃ - a₃b₂, a₃b₁ - a₁b₃, a₁b₂ - a₂b₁)
• 5. Magnitude: |a| = √(a₁² + a₂² + a₃²)
• 6. Angle between vectors: cosθ = a · b / (|a| |b|)
• 7. Unit vector: â = a / |a|
• 8. Vector projection: proj_b a = (a · b) / |b|² × b