Chapter 13, Problem 9CT

a.

To determine

To find: the value of $\stackrel{\rightharpoonup }{PQ}$ .

Answer to Problem 9CT

The value of $\stackrel{\rightharpoonup }{PQ}$ is $\left(6,-4\right)$ .

Explanation of Solution

Given information: The points are $P\left(-2,5\right)\&Q\left(4,1\right)$ .

Calculation:

  $\begin{array}{l}\stackrel{\rightharpoonup }{PQ}=\left(x_2-x_1,y_2-y_1\right)\\ \stackrel{\rightharpoonup }{PQ}=\left(4-\left(-2\right),1-5\right)\\ \stackrel{\rightharpoonup }{PQ}=\left(6,-4\right)\end{array}$

b.

To determine

To find: the value of $\left|\stackrel{\rightharpoonup }{PQ}\right|$ .

Answer to Problem 9CT

The value of $\left|\stackrel{\rightharpoonup }{PQ}\right|$ is $\sqrt{52}$ .

Explanation of Solution

Given information: The points are $P\left(-2,5\right)\&Q\left(4,1\right)$ .

Calculation:

  $\begin{array}{l}\left|\stackrel{\rightharpoonup }{PQ}\right|=\sqrt{\left({\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2\right)}\\ \left|\stackrel{\rightharpoonup }{PQ}\right|=\sqrt{\left({\left(4-\left(-2\right)\right)}^2+{\left(1-5\right)}^2\right)}\\ \left|\stackrel{\rightharpoonup }{PQ}\right|=\sqrt{\left(36+16\right)}\\ \left|\stackrel{\rightharpoonup }{PQ}\right|=\sqrt{52}\end{array}$