First slide

Vectors

Question

The position vectors of two balls are given by
$\vec{r_{1}} = 2 (m) \hat{i} + 7 (m) \hat{j}$
$\vec{r_{2}} = - 2 (m) \hat{i} + 4 (m) \hat{j}$
What is the distance between the two balls?

Moderate

A

4 m
B

4.5 m
C

5 m
D

3 m

Solution

$\vec{r_{1}} = 2 (m) \hat{i} + 7 (m) \hat{j}$
$\vec{r_{2}} = - 2 m \hat{i} + 4 m \hat{j}$
$∴$ $\vec{r_{1}} - \vec{r_{2}} = [2 - (- 2)] \hat{i} + (7 - 4) \hat{j}$
$∴$ $| \vec{r_{1}} - \vec{r_{2}} | = \sqrt{{(4)}^{2} + {(3)}^{2}} = \sqrt{{(5)}^{2}} = 5 m$

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