# 11a. Vector basics

The following questions illustrate the key concepts needed in this topic. See if you can answer them.
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Notation
In print, vectors are typeset in bold, like $\mathbf{a}$. In writing, we usually put a tilde underneath, like $\underset{\sim}{a}$.
$\overrightarrow{AB}$ is the vector represented by the directed line segment $AB$.
$| \textbf{ a }|$: the magnitude of $\mathbf{a}$.
$\hat{\mathbf{a}}$: a unit vector in the direction of $\mathbf{a}$.
$\mathbf{i} = \begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix}, \, \mathbf{j} = \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix}, \, \mathbf{k} = \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix}$.
Ratio theorem formula (provided)
The point dividing $AB$ in the ratio $\lambda:\mu$ has position vector $\displaystyle \frac{\mu \mathbf{a} + \lambda \mathbf{b}}{\lambda + \mu}$