Study guide and
3 practice problems
on:
Finding the unit vector in the same direction as another vector
$\newcommand{\bfA}{\mathbf{A}}$ $\newcommand{\bfB}{\mathbf{B}}$ $\newcommand{\bfC}{\mathbf{C}}$ $\newcommand{\bfF}{\mathbf{F}}$ $\newcommand{\bfI}{\mathbf{I}}$ $\newcommand{\bfa}{\mathbf{a}}$ $\newcommand{\bfb}{\mathbf{b}}$ $\newcommand{\bfc}{\mathbf{c}}$ $\newcommand{\bfd}{\mathbf{d}}$ $\newcommand{\bfe}{\mathbf{e}}$ $\newcommand{\bfi}{\mathbf{i}}$ $\newcommand{\bfj}{\mathbf{j}}$ $\newcommand{\bfk}{\mathbf{k}}$ $\newcommand{\bfn}{\mathbf{n}}$ $\newcommand{\bfr}{\mathbf{r}}$ $\newcommand{\bfu}{\mathbf{u}}$ $\newcommand{\bfv}{\mathbf{v}}$ $\newcommand{\bfw}{\mathbf{w}}$ $\newcommand{\bfx}{\mathbf{x}}$ $\newcommand{\bfy}{\mathbf{y}}$ $\newcommand{\bfz}{\mathbf{z}}$
To find the unit vector in the same direction as $\bfx$, divide $\bfx$ by its length.
That is to say, $\text{dir } \bfx = \frac{\bfx}{| \bfx |}$, is the unit vector in the same direction as $\bfx$.
Related topics
Direction of a vector
(9 problems)
Length of a vector
(32 problems)
Vectors
(55 problems)
Multivariable calculus
(147 problems)
Practice problems
Find a unit vector in the direction of $\langle 1, 1 \rangle$.
Solution
Find a unit vector perpendicular to $\langle 1, 1, 1\rangle$ and $\langle 1, 0, 1 \rangle.$
Solution
Find all the vectors in 3d that have unit length and are perpendicular to $$\Bigl(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 0 \Bigr) \ \text{ and } \ \Bigl(0, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} \Bigr).$$
Solution