Question

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

role="math" localid="1646909539329" $P=(0,-2);Q=(-1,1)$

Short answer

$$\begin{gathered} v=-1+3j \\ \parallel v\parallel =\sqrt{10} \end{gathered}$$

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:

$P=(0,-2);Q=(-1,1)$

Step 2. Find the position of the 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,

$\begin{array}{r}\mathbf{v}=[P,Q]\\ =\left[\right(-1-0),(1-(-2)\left)\right]\\ =(-1,3)\\ =-i+3j\end{array}$

Step 4. Calculate the magnitude

$\begin{array}{r}\parallel \mathbf{v}\parallel =\sqrt{(-1{)}^2+(3{)}^2}\\ =\sqrt{1+9}\\ =\sqrt{10}\\ \end{array}$