## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 6 - Section 6.7 - The Dot Product - Exercise Set - Page 792: 8

#### Answer

$\mathbf{v}\cdot \mathbf{w}=0$ and $\mathbf{v}\cdot \mathbf{v}=1$

#### Work Step by Step

The dot product, $\mathbf{v}\cdot \mathbf{w}$ as, Solve ahead to get the result as, \begin{align} & \mathbf{v}\cdot \mathbf{w}=0\left( 1 \right)-5\left( 0 \right)+0+0 \\ & =0 \end{align} The dot product, $\mathbf{v}\cdot \mathbf{v}$ as, \begin{align} & \mathbf{v}\cdot \mathbf{v=}\left( \mathbf{i}+0\mathbf{j} \right)\cdot \left( \mathbf{i}+0\mathbf{j} \right) \\ & =\left( 1 \right)\mathbf{i}\cdot \left( 1 \right)\mathbf{i+}\left( 1 \right)\mathbf{i}\cdot \left( 0 \right)\mathbf{j+}\left( 0 \right)\mathbf{j}\cdot \left( 1 \right)\mathbf{i+}\left( 0 \right)\mathbf{j}\cdot \left( 0 \right)\mathbf{j} \\ & =1\left( \mathbf{i}\cdot \mathbf{i} \right)+0\left( \mathbf{i}\cdot \mathbf{j} \right)+0\left( \mathbf{j}\cdot \mathbf{i} \right)+0\left( \mathbf{j}\cdot \mathbf{j} \right) \\ & =1\left( 1 \right)+0+0+0 \end{align} Solve ahead to get the result as, \begin{align} & \mathbf{v}\cdot \mathbf{v}=1\left( 1 \right)+0+0+0 \\ & =1 \end{align}

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