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Q26.

Expert-verifiedFound in: Page 646

Book edition
7th Edition

Author(s)
James Stewart, Lothar Redlin, Saleem Watson

Pages
948 pages

ISBN
9781337067508

**The Component of $u$ along $v$**

**Find the component of $u$ along $v$.**

**$\mathbf{u}=\u27e8-3,5\u27e9,\mathbf{v}=\u27e81/\sqrt{2},1/\sqrt{2}\u27e9$**

The component is $\sqrt{2}$

Vectors are given as-

$\mathbf{u}=\u27e8-3,5\u27e9,v=\u27e81/\sqrt{2},1/\sqrt{2}\u27e9$

The dot product of two vectors $u$ and $v$ can be defined as-

$u\xb7v={a}_{1}{b}_{1}+{a}_{2}{b}_{2}$

Where $u=\left({a}_{1},{a}_{2}\right)\&v=\left({b}_{1},{b}_{2}\right)$

If $u$ and $v$ are two vectors then the component of $u$ along $v$ can be defined as $com{p}_{v}u=\frac{u\xb7v}{\left|v\right|}$

Use the formula of components of $u$ along $v$ and the dot product of vectors.

Component of $u$ along $v$,

$\begin{array}{l}{\mathrm{comp}}_{v}u=\frac{u\cdot v}{\left|v\right|}\\ =\frac{-3\left\{\frac{1}{\sqrt{2}}\right\}+5\left\{\frac{1}{\sqrt{2}}\right\}}{\sqrt{{\left\{\frac{1}{\sqrt{2}}\right\}}^{2}+{\left\{\frac{1}{\sqrt{2}}\right\}}^{2}}}\\ =\frac{\sqrt{2}}{1}\\ =\sqrt{2}\end{array}$

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