Question

The vector v is represented by the directed line segment $\underset{PQ}{\to }$Write v in the form ai + bj and find $\parallel v\parallel$.

role="math" localid="1646907960914" $P=(-1,2);Q=(3,-6)$

Short answer

$$\begin{gathered} v=2i-4j \\ \parallel v\parallel =2\sqrt{5} \end{gathered}$$

Step-by-step solution

Step 1. Given information

We have to write the vector v in the form $ai+bj$and also we have to find $\parallel v\parallel$.

Given points are:

$P=(-1,2);Q=(3,-6)$

Step 2. Find the position of vector

To find the position of the vector,

we know that,

$\begin{array}{c}\mathbf{v}=\overrightarrow{P_1{P}_2}\end{array}$

where,

$P=(x,y)$

it can be written as:

Step 3. Find the vector v

For the points we have,

$\begin{array}{r}\mathbf{v}=[P,Q]\\ =\left[\right(3-1),(-6-(-2)\left)\right]\\ =(2,-4)\\ =2i-4j\end{array}$

Step 4. Calculate the magnitude

$\begin{array}{r}\parallel \mathbf{v}\parallel =\sqrt{(2{)}^2+(-4{)}^2}\\ =\sqrt{4+16}\\ =\sqrt{20}\\ =2\sqrt{5}\end{array}$