## Chapter 2SCALARS AND VECTORS

‘The moral of *that* is, “Take care of the sense and the sounds will take care of themselves”.’

LEWIS CARROLL, *Alice in Wonderland*

### 2·01. Cartesian coordinates: summation convention.

Any physical measurement is the assignment of a single magnitude. Physics may be defined as the study of the relations between magnitudes, so that from one set of measurements other sets, given the conditions of observation, can be predicted. The most elementary measures, except for simple counting, are those of distance. Now we saw that distances along the same straight line are found experimentally to be additive in a definable sense, and to satisfy the associative and commutative laws of addition. But when two distances are not along ...