Chapter 6.4, Problem 72E

a.

To determine

Dot product $u.v$ and explain its meaning.

Answer to Problem 72E

  $u.v=19105$

Explanation of Solution

Given information:

  $\begin{array}{l}u=\left(3240,2450\right)\\ v=\left(3.25,3.50\right)\end{array}$

Formula used: -

  $u.v=a_1{a}_2+b_1{b}_2$

  $\begin{array}{l}u.v=a_1{a}_2+b_1{b}_2\\ u.v=\left(3240\right)\left(3.25\right)+\left(2450\right)\left(3.50\right)\\ u.v=10530+8575\\ \boxed{u.v=19105}\end{array}$

This dot product of u and v shows the total money got by selling hamburgers and hot dog in a week.

b.

To determine

Vector operation used to increase wages by 2.5 percent.

Answer to Problem 72E

Vector operation to increase the wages by 2.5 percent, i.e. $1.025v=\left(3.33,3.58\right)$

Explanation of Solution

Given information:

  $v=\left(3.25,3.50\right)$

Formula used: -

  $\begin{array}{l}cv=c\left(a,b\right)\\ cv=\left(ca,cb\right)\end{array}$

Vector operation to increase the wages by 2.5 percent is by multiplying v vector by 1.025

  $\begin{array}{l}1.025v=1.025v\left(3.25,3.50\right)\\ \boxed{1.025v=\left(3.33,3.58\right)}\end{array}$