Study guide and
4 practice problems
on:
Definition of the direction of a vector
$\newcommand{\bfA}{\mathbf{A}}$ $\newcommand{\bfB}{\mathbf{B}}$ $\newcommand{\bfC}{\mathbf{C}}$ $\newcommand{\bfF}{\mathbf{F}}$ $\newcommand{\bfI}{\mathbf{I}}$ $\newcommand{\bfa}{\mathbf{a}}$ $\newcommand{\bfb}{\mathbf{b}}$ $\newcommand{\bfc}{\mathbf{c}}$ $\newcommand{\bfd}{\mathbf{d}}$ $\newcommand{\bfe}{\mathbf{e}}$ $\newcommand{\bfi}{\mathbf{i}}$ $\newcommand{\bfj}{\mathbf{j}}$ $\newcommand{\bfk}{\mathbf{k}}$ $\newcommand{\bfn}{\mathbf{n}}$ $\newcommand{\bfr}{\mathbf{r}}$ $\newcommand{\bfu}{\mathbf{u}}$ $\newcommand{\bfv}{\mathbf{v}}$ $\newcommand{\bfw}{\mathbf{w}}$ $\newcommand{\bfx}{\mathbf{x}}$ $\newcommand{\bfy}{\mathbf{y}}$ $\newcommand{\bfz}{\mathbf{z}}$
The direction of a vector $\mathbf{x}$ is defined by $\text{dir } \mathbf{x} = \frac{\mathbf{x}}{| \mathbf{x} | }.$
Related topics
Direction of a vector
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Vectors
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Multivariable calculus
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Practice problems
A river flows with speed $10$ m/s in the northeast direction. A particular boat can propel itself at speed $20$ m/s relative to the water. In which direction should the boat point in order to travel due west.?
Solution
Find the vector of length 2 in the direction of $\langle 1,-1 \rangle$.
Solution
Let $c$ be a nonzero scalar. Does $c \ \mathbf{x}$ have the same direction as $\mathbf{x}$?
Solution
Compute the vector projection of $\bfi$ onto $\bfi + \bfj$.
Solution