Question

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

role="math" localid="1646783809785" $P=(3,2,-1);Q=(5,6,0)$

Short answer

The position vector is$\mathit{\nu }=2\mathit{i}+4\mathit{j}+\mathit{k}$

Step-by-step solution

Step 1. Given data  

Initial point is$P(x_1,y_1,z_1)=(3,2,-1)$

Terminal point is$Q(x_2,y_2,z_2)=(5,6,0)$

Step 2. Position Vector 

Use position vector formula

$$\begin{gathered} \mathit{\nu }=(x_2-x_1)\mathit{i}+(y_2-y_1)\mathit{j}+(z_2-z_1)\mathit{k} \\ \mathit{\nu }=(5-3)\mathit{i}+(6-2)\mathit{j}+(0-\left(-1\right))\mathit{k} \\ \mathit{\nu }=2\mathit{i}+4\mathit{j}+\mathit{k} \end{gathered}$$

So position vector is$\mathit{\nu }=2\mathit{i}+4\mathit{j}+\mathit{k}$