Mathematics - Linear Algebra - Vectors and vector operations - Vector Operations

10 steps: (1) A vector has magnitude and direction. v=(3,4) means 3 in x, 4 in y. (2) Magnitude: |v| = √(3²+4²) = 5. (3) Addition: (a₁,a₂)+(b₁,b₂) = (a₁+b₁, a₂+b₂). (4) Scalar multiplication: c·(a₁,a₂) = (ca₁,ca₂). Stretches/shrinks. (5) Unit vector: v/|v|. Direction only, magnitude 1. (6) DOT PRODU