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Expert-verified Found in: Page 801 ### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861 # Find $||v||$ and find the unit vector in the direction of $v$.$v=\left(3,-4\right)$

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 $\frac{1}{5}\left(3,-4\right)$.

See the 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.

$||v||=\sqrt{{a}^{2}+{b}^{2}}\phantom{\rule{0ex}{0ex}}=\sqrt{{3}^{2}+{\left(-4\right)}^{2}}\phantom{\rule{0ex}{0ex}}=\sqrt{9+16}\phantom{\rule{0ex}{0ex}}=\sqrt{25}\phantom{\rule{0ex}{0ex}}=5$

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

$\frac{1}{||v||}v=\frac{1}{5}\left(3,-4\right)\phantom{\rule{0ex}{0ex}}$ ### Want to see more solutions like these? 