Study guide and
5 practice problems
on:
Definition of a unit vector
$\newcommand{\bfA}{\mathbf{A}}$ $\newcommand{\bfB}{\mathbf{B}}$ $\newcommand{\bfC}{\mathbf{C}}$ $\newcommand{\bfF}{\mathbf{F}}$ $\newcommand{\bfI}{\mathbf{I}}$ $\newcommand{\bfa}{\mathbf{a}}$ $\newcommand{\bfb}{\mathbf{b}}$ $\newcommand{\bfc}{\mathbf{c}}$ $\newcommand{\bfd}{\mathbf{d}}$ $\newcommand{\bfe}{\mathbf{e}}$ $\newcommand{\bfi}{\mathbf{i}}$ $\newcommand{\bfj}{\mathbf{j}}$ $\newcommand{\bfk}{\mathbf{k}}$ $\newcommand{\bfn}{\mathbf{n}}$ $\newcommand{\bfr}{\mathbf{r}}$ $\newcommand{\bfu}{\mathbf{u}}$ $\newcommand{\bfv}{\mathbf{v}}$ $\newcommand{\bfw}{\mathbf{w}}$ $\newcommand{\bfx}{\mathbf{x}}$ $\newcommand{\bfy}{\mathbf{y}}$ $\newcommand{\bfz}{\mathbf{z}}$
A unit vector is a vector with length 1.
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Practice problems
Sketch all the unit vectors in 3d that have an angle of $\pi/6$ with respect to the vector $\bfi$.
Solution
Sketch all the unit vectors in 2d that have an angle of $\pi/4$ with respect to the vector $\bfi$.
Solution
For what value(s) of $c$ is $c (\textbf{i} + \textbf{j} + \textbf{k})$ a unit vector?
Solution
Find a unit vector perpendicular to $\langle 1, 1, 1\rangle$ and $\langle 1, 0, 1 \rangle.$
Solution
Write down the vector field $\mathbf{F}(x,y)$ whose value at $(x,y)$ is of unit length and points toward $(1,0)$.
Solution