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Q 37,

Expert-verifiedFound in: Page 801

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

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

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

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

$\frac{1}{||v||}v=\frac{1}{5}\left(3,-4\right)\phantom{\rule{0ex}{0ex}}$

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