Chapter 13.4, Problem 27WE

To determine

To find: The magnitude of the force.

Answer to Problem 27WE

The magnitude of the force $=10$

Explanation of Solution

Given information: An object being pulled by the forces $\overrightarrow{KX}=\left(-1,5\right)$ and $\overrightarrow{KY}=\left(7,3\right)$ .

Formula used: Vectors can be added by following simple rule $\left(a,b\right)+\left(c,d\right)=\left(a+c,b+d\right)$ .

Calculation: An object being pulled by the forces $\overrightarrow{KX}=\left(-1,5\right)$ and $\overrightarrow{KY}=\left(7,3\right)$ .

Vectors can be added by following simple rule $\left(a,b\right)+\left(c,d\right)=\left(a+c,b+d\right)$ .

  $\begin{array}{l}\overrightarrow{KX}+\overrightarrow{KY}=\left(-1,5\right)+\left(7,3\right)\\ \overrightarrow{KX}+\overrightarrow{KY}=\left(6,8\right)\\ \overrightarrow{KX}+\overrightarrow{KY}=\overrightarrow{XY}\end{array}$

The magnitude of the force $=\sqrt{36+64}$ .

The magnitude of the force $=10$