Question

In Problems, the vector v has initial point P and terminal point Q. Write v in the form$a\mathit{i}+b\mathit{j}+c\mathit{k}$; that is, find its position vector.
localid="1646771777507" $P=(-3,2,0);Q=(6,5,-1)$

Short answer

The position vector is$\mathit{\nu }=9\mathit{i}+3\mathit{j}-1\mathit{k}$

Step-by-step solution

Step 1. Given data 

Initial point is$P(x_1,y_1,z_1)=(-3,2,0)$

Terminal point is$Q(x_2,y_2,z_2)=(6,5,-1)$

Step 2. Position Vector 

Use position vector formula

$$\begin{gathered} \mathit{\nu }=(x_2-x_1)\mathit{i}+(y_2-y_1)\mathit{j}+(z_2-z_1)\mathit{k} \\ \mathit{\nu }=(6-(-3\left)\right)\mathit{i}+(5-2)\mathit{j}+(-1-0)\mathit{k} \\ \mathit{\nu }=9\mathit{i}+3\mathit{j}-1\mathit{k} \end{gathered}$$

So position vector is$\mathit{\nu }=9\mathit{i}+3\mathit{j}-1\mathit{k}$