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Chapter 3 Vectors

Many quantities in physics have both a magnitude and a direction and follow completely different rules of addition and multiplication than those for regular numbers. These quantities are called vectors. Analytically, vectors are usually processed using components along Cartesian axes. In the \(xy\) plane, the polar representation of these components gives us magnitude and direction of the vector. In full \(xyz\) space, spherical representation gives us magnitude and direction.

We denote a vector quantity by a symbol with an arrow over the symbol, e.g., symbol for a position vector could be \(\vec r\text{.}\) The symbol stands for both the magnitude and direction. If we mean just the magnitude, we omit the overhead arrow from the symbol, e.g., we would write \(r \) for the magnitude of vector \(\vec r \text{,}\) \(v \) for the magnitude of vector \(\vec v \text{,}\) etc.

You will use vectors in the rest of the book. Therefore, you should get very familiar with all the algebra that goes with them.