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Expert-verified Found in: Page 646 ### Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508 # Dot ProductsFind the indicated quantity, assuming that $\mathbf{u}=2\mathbf{i}+\mathbf{j},\mathbf{v}=\mathbf{i}-3\mathbf{j}&\mathbf{w}=3\mathbf{i}+4\mathbf{j}$$\left(\mathbf{u}·\mathbf{v}\right)\left(\mathbf{u}·\mathbf{w}\right)$

The required value of dot product is $-10$

See the step by step solution

## Step 1. Given information

Vectors are given as

$\begin{array}{l}u=2i+j\\ v=i-3j\\ w=3i+4j\end{array}$

## Step 2. Concept used

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

$u·v={a}_{1}{b}_{1}+{a}_{2}{b}_{2}$

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

Properties of the dot product of vectors

$u·u=|u{|}^{2}$

Transform the required expression and find the value using the dot product of vectors.

## Step 3. Calculation

Using Properties of the dot product of vectors,

$\begin{array}{l}\left(u\cdot v\right)\left(u\cdot w\right)=\left[\left(2\right)\left(1\right)+\left(1\right)\left(-3\right)\right]×\left[\left(2\right)\left(3\right)+\left(1\right)\left(4\right)\right]\\ =\left(2-3\right)×\left(6+4\right)\\ =\left(-1\right)×\left(10\right)\\ =-10\end{array}$ ### Want to see more solutions like these? 