Question

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

$P=(0,0);Q=(-3,-5)$

Short answer

The position vector is$-3\hat{i}-5\hat{j}$.

Step-by-step solution

Step 1. Given Information

We are given initial point as $P=(0,0)$and terminal point as $Q=(-3,-5)$and we need to find the position vector.

Step 2. Finding the position vector

The position vector v with initial point $(a_1,b_1)$and terminal point $(a_2,b_2)$is given by $v=(a_2-a_1)\hat{i}+(b_2-b_1)\hat{j}$.

Substituting the values we get the required position vector

$$\begin{gathered} \therefore v=(-3-0)\hat{i}+(-5-0)\hat{j} \\ \Rightarrow v=-3\hat{i}-5\hat{j} \end{gathered}$$