Chapter 13.4, Problem 5WE

To determine

To make a sketch, then find $\overrightarrow{AB}$ and $\left|\overrightarrow{AB}\right|$ of a points $A\left(3,5\right)$ and $B\left(-1,7\right)$ .

Answer to Problem 5WE

The required solution are,

Sketch is,

  

  $\overrightarrow{AB}=\left(-4,2\right)$ and $\left|\overrightarrow{AB}\right|=2\sqrt{5}$ .

Explanation of Solution

Given information: The points are $A\left(3,5\right)$ and $B\left(-1,7\right)$ .

Calculation: The required solution are obtained as,

The sketch of points $A\left(3,5\right)$ and $B\left(-1,7\right)$ is,

  

  $\overrightarrow{AB}$ obtained as,

  $\overrightarrow{AB}=\left(x_2-x_1,y_2-y_1\right)=\left(-1-3,7-5\right)=\left(-4,2\right)$

  $\left|\overrightarrow{AB}\right|$ obtained as,

  $\left|\overrightarrow{AB}\right|=\sqrt{x^2+y^2}=\sqrt{{\left(-4\right)}^2+{\left(2\right)}^2}=\sqrt{20}=2\sqrt{5}$

Hence, the required solution are, $\overrightarrow{AB}=\left(-4,2\right)$ and $\left|\overrightarrow{AB}\right|=2\sqrt{5}$ .