Solve the problem
-A force is given by the vector $\mathbf { F } = 6 \mathbf { i } + 7 \mathbf { j }$. The force moves an object along a straight line from the point $( 6,4 )$ to the point $( 19,18 )$. Find the work done if the distance is measured in feet and the force is measured in pounds.
A) $176 \mathrm { ft } - \mathrm { lb }$
B) $- 20 \mathrm { ft } - \mathrm { lb }$
C) $- 176 \mathrm { ft } - \mathrm { lb }$
D) $175 \mathrm { ft } - \mathrm { lb }$

Question

Quizplus · Accepted Answer

The work done by a force is given by the dot product of the force vector and the displacement vector. The displacement vector is $\mathbf{d} = (19 - 6)\mathbf{i} + (18 - 4)\mathbf{j} = 13\mathbf{i} + 14\mathbf{j}$. The dot product of $\mathbf{F} = 6\mathbf{i} + 7\mathbf{j}$ and $\mathbf{d} = 13\mathbf{i} + 14\mathbf{j}$ is $6*13 + 7*14 = 78 + 98 = 176$. Therefore, the work done is $176 \mathrm{ft-lb}$.

Solve the Problem -A Force Is Given by the Vector F=6i+7j\mathbf { F } = 6 \mathbf { i } + 7 \mathbf { j }F=6i+7j

Solve the Problem
-A Force Is Given by the Vector $\mathbf { F } = 6 \mathbf { i } + 7 \mathbf { j }$