The Magnitude of a Vector

Remembering that the magnitude of the vector is one of its defining features, this is often something that isis interesting or useful to know, even when we only have the component form of a vector.

Fortunately, this is something we can readily calculate using the Pythgorean Theorem. In two dimensions, we can construct a right-angled triangle using the breakdown into horizontal and vertical components. We will find that the magnitude of the vector $\overrightarrow{X} = a\underset{\sim}{i} + b\underset{\sim}{j}$, which we write as $\left|\overrightarrow{X}\right|$ is given by

$$\left|\overrightarrow{X}\right| = \sqrt{a^2 + b^2}$$

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