Vector Operations

Build two vectors from their components and watch the sum appear tip-to-tail. Read off the magnitude √(x²+y²), the direction angle, and a scalar multiple c·a.

→ a → b → a+b → c·a

Vector a = ⟨a₁, a₂⟩

a₁ 4

a₂ 2

Vector b = ⟨b₁, b₂⟩

b₁ -1

b₂ 5

Scalar multiple c·a

c 1.5

Try: set c = −1 — the purple vector flips to point exactly opposite a with the same length. Then make b = −a and watch the sum a+b collapse to the zero vector at the origin.