Chapter 6.4, Problem 71E

a.

To determine

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

Answer to Problem 71E

  $u.v=39761.25$

Explanation of Solution

Given information:

  $\begin{array}{l}u=\left(1225,2445\right)\\ v=\left(12.00,10.25\right)\end{array}$

Formula used: -

  $u.v=a_1{a}_2+b_1{b}_2$

  $\begin{array}{l}u.v=a_1{a}_2+b_1{b}_2\\ u.v=\left(1225\right)\left(12\right)+\left(2445\right)\left(10.25\right)\\ u.v=14700+25061.25\\ \boxed{u.v=39761.25}\end{array}$

This dot product of u and v shows the total amount of wage paid to the employees.

b.

To determine

Vector operation used to increase wages by 2 percent.

Answer to Problem 71E

Vector operation to increase the wages by 2 percent, i.e. $1.02v=\left(12.24,10.45\right)$

Explanation of Solution

Given information:

  $v=\left(12.00,10.25\right)$

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 percent is by multiplying v vector by 1.02

  $\begin{array}{l}1.02v=1.02\left(12.00,10.25\right)\\ \boxed{1.02v=\left(12.24,10.45\right)}\end{array}$