## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 6 - Section 6.7 - The Dot Product - Exercise Set - Page 793: 59

#### Answer

The work done is 40 foot-pounds

#### Work Step by Step

Here, the object moves along the straight line, such that the angle between the force and direction of motion is ${{0}^{\circ }}$. The object is moved from point $\left( 4,9 \right)$ to $\left( 10,20 \right)$. Therefore, the point to which the object has traveled is: \begin{align} & \mathbf{AB}=\left[ \left( 10,20 \right)-\left( 4,9 \right) \right] \\ & =\left[ \left( 10-4 \right),\left( 20-9 \right) \right] \\ & =\left( 6,11 \right) \end{align} $\mathbf{AB}=6\mathbf{i}+11\mathbf{j}$ …… (2) Now, as it is known that: $\mathbf{W}=\mathbf{F}\cdot \mathbf{AB}$ …… (3) Substituting equation (1) and (2) in equation (3), \begin{align} & \mathbf{W}=\left( 3\mathbf{i}+2\mathbf{j} \right)\left( 6\mathbf{i}+11\mathbf{j} \right) \\ & =\left[ \left( 3\times 6 \right)+\left( 11\times 2 \right) \right] \\ & =18+22 \\ & =40 \end{align}

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