Chapter 13.4, Problem 1WE

To determine

To make a sketch, then find $\overrightarrow{AB}$ and $\left|\overrightarrow{AB}\right|$ of a points $A\left(1,1\right)$ and $B\left(5,4\right)$ .

Answer to Problem 1WE

The required solution are,

Sketch is,

  

  $\overrightarrow{AB}=\left(4,3\right)$ and $\left|\overrightarrow{AB}\right|=5$ .

Explanation of Solution

Given information: The points are $A\left(1,1\right)$ and $B\left(5,4\right)$ .

Calculation: The required solution are obtained as,

The sketch of points $A\left(1,1\right)$ and $B\left(5,4\right)$ is,

  

  $\overrightarrow{AB}$ obtained as,

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

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

  $\left|\overrightarrow{AB}\right|=\sqrt{x^2+y^2}=\sqrt{4^2+3^2}=\sqrt{25}=5$

Hence, the required solution are, $\overrightarrow{AB}=\left(4,3\right)$ and $\left|\overrightarrow{AB}\right|=5$ .