Vectors in Two Dimensions (Copy)

13 Vectors – Cheat Sheet

13.1 Vector Notation

• Common forms:
  (a, b), ⟨a, b⟩, AB, p, ai − bj
• Position vector OA: vector from origin O to point A.

13.2 Position & Unit Vectors

• Position vector: from origin to point P(x, y) is (x, y).
• Unit vector in the direction of a:
  â = a / |a|

13.3 Magnitude, Addition, Subtraction, Scalar Multiplication

• Magnitude of a = (x, y): |a| = √(x² + y²)
• Addition: (x₁, y₁) + (x₂, y₂) = (x₁ + x₂, y₁ + y₂)
• Subtraction: (x₁, y₁) − (x₂, y₂) = (x₁ − x₂, y₁ − y₂)
• Scalar multiplication: k × (x, y) = (kx, ky)
• Equating vectors: equate components separately.

13.4 Resultant & Velocity Vectors

• Resultant vector: R = v₁ + v₂ (+ more if needed).
• Magnitude of resultant: |R| = √(Rₓ² + Rᵧ²)
• Velocity vector: displacement / time.
• Use vector addition for velocity composition.