Question

In Problems, the vector v has initial point P and terminal point Q. Write v in the form ai + bj; that is, find its position vector.

$P=\left(3,2\right);Q=\left(5,6\right)$

Short answer

v = $\left(2i+4j\right)$

The position vector is :$\left(2,4\right)$

Step-by-step solution

Step 1. Given information

Initial point P$\left(3,2\right)$

Terminal point Q$\left(5,6\right)$

We know that if P$\left(x_1,y_1\right)$is the initial point and Q$\left(x_2,y_2\right)$is the terminal point then the position vector is

localid="1646708398743" $v=\left(\left(x_2-x_1\right),\left(y_2-y_1\right)\right)$

step 2. Calculating the v 

As $v=\left(\left(x_2-x_1\right),\left(y_2-y_1\right)\right)$

so for P and Q

$$\begin{gathered} v=\left(\left(5-3\right),\left(6-2\right)\right) \\ v=\left(2,4\right) \end{gathered}$$

Step 3. Calculating the position vector 

We know that if $\left(x,y\right)$represent the position of point v then in vector form

$$\begin{gathered} v=\left(x,y\right)=x\left(1,0\right)i+y\left(0,1\right)j \\ v=xi+yj \end{gathered}$$

Now for v(2,4)

$v=2i+4j$