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Mathematics · Ch 8 — Vector Algebra-I

Scalars and Vectors

8.2

Scalars and Vectors

Scalars vs vectors. A scalar is a quantity that is completely described once you know how much of it there is — its magnitude, and nothing else. Distance, length, speed, temperature, voltage, mass, pressure and work are all scalars: '55 kg' or '40∘40^\circC' is a complete description.

A vector is a quantity that needs both a magnitude and a direction to be fully described, and for that reason it is naturally pictured as a directed line segment. Force, displacement, and velocity are vectors: knowing a force is '1010 N' tells you nothing about which way it pushes. …

Figure 8.1Tail and tip of a vector

What this figure shows. A directed segment from initial point A (tail) to terminal point B (tip), labelled vector a, showing |a| as the length AB. …