Vectors: magnitude, addition and scalar multiples

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Useful for: IB Math AA HL AP® Precalculus

Learn it A vector has a size (magnitude) and a direction. In components, u = (a, b) has magnitude |u| = √(a² + b²). Add vectors component by component; multiplying by a scalar k multiplies each component by k.

Example: A plane flies 300 km/h north while the wind blows 40 km/h east. Ground speed?

Velocity = (40, 300).
|v| = √(40² + 300²) ≈ 302.7 km/h.

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