Vector Operations Calculator

Calculate vector operations including magnitude, addition, subtraction, scalar multiplication, dot product, and check collinearity and perpendicularity relationships.

Vector Calculator

Choose calculation type and enter vector coordinates

Calculation Type

Vector = (x, y)

Current Operation:

|x, y|

Calculation Methods

Magnitude: |v| = √(x² + y²), Unit vector: v/|v|

Addition: (x₁, y₁) + (x₂, y₂) = (x₁+x₂, y₁+y₂)

Subtraction: (x₁, y₁) - (x₂, y₂) = (x₁-x₂, y₁-y₂)

Scalar Multiplication: λ(x, y) = (λx, λy)

Collinearity: x₁y₂ - x₂y₁ = 0

Perpendicularity: x₁x₂ + y₁y₂ = 0

Dot Product: a·b = x₁x₂ + y₁y₂

Related Resources

Vector Knowledge Summary

Key Relationships:

• Collinear vectors: Cross product = 0
• Perpendicular vectors: Dot product = 0
• Unit vector has magnitude = 1
• Zero vector is parallel to all vectors