Question

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

Short answer

$$\begin{gathered} v=\left(9,3\right) \\ Positionvector\left(9i+3j\right) \end{gathered}$$

Step-by-step solution

Step1. Given Information

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

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

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

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

Step 2. Calculating the position vector 

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

for P (-3,2)

and Q (6,5)

$$\begin{gathered} v=\left(\left(6-\left(-3\right)\right),\left(5-2\right)\right) \\ v=\left(9,3\right) \end{gathered}$$

in vector form $v=9i+3j$