Question

Find $||v||$and find the unit vector in the direction of $v$.

$v=\left(3,-4\right)$

Short answer

The norm of the vector $v=\left(3,-4\right)$is $5$ and the unit vector in the direction of$v=\left(3,-4\right)$is$\frac{1}{5}\left(3,-4\right)$.

Step-by-step solution

Step 1. Given information . 

We have given vector$v=\left(3,-4\right)$.

Step 2. Find the norm of the vector and unit vector in the direction of v.

$$\begin{gathered} ||v||=\sqrt{a^2+b^2} \\ =\sqrt{3^2+{\left(-4\right)}^2} \\ =\sqrt{9+16} \\ =\sqrt{25} \\ =5 \end{gathered}$$

The unit vector in the direction of $v$is $\frac{1}{||v||}v$.

$\frac{1}{||v||}v=\frac{1}{5}\left(3,-4\right)$