Vector Operations

Calculus 2 · Axiom Academy

Add, scalar-multiply, subtract, and measure two plane vectors — component by component, with the geometry drawn alongside. Given the two plane vectors below, compute the sum , the combination , and the magnitude . Nice work — you ran the three core operations on and . The pattern: Addition: add matching components — . Here , the parallelogram diagonal. Scalar multiple: scale every component — . So , twice as long, same direction. Subtraction: subtract componentwise (add the negative) — . Magnitude: , the Pythagorean length — never negative. These four moves are the bedrock of multivariable calculus — you reach for them constantly with velocity, acceleration, gradients, and vector fields.

This is the written version of the interactive lesson above. See the full Calculus 2 course.