## Fundamentals of Physics Extended (10th Edition)

Published by Wiley

# Chapter 4 - Motion in Two and Three Dimensions - Problems: 3

#### Answer

$(-2\hat{i}+6\hat{j}-10\hat{k})\ m$

#### Work Step by Step

Given: Displacement $\vec{\Delta r} = 2\hat{i}-3\hat{j}+6\hat{k}$ Ending position vector $\vec{r_f}=3\hat{j}-4\hat{k}$ Let the initial position vector be $r_i$. We know that: $\vec{\Delta r }= \vec{r_f}-\vec{r_i}$ This can be rearranged as: $\vec{r_i} =\vec{r_f} - \vec{\Delta r}$ Substituting and solving: $\vec{\Delta r} =3\hat{j}-4\hat{k} - (2\hat{i}-3\hat{j}+6\hat{k})$ $\vec{\Delta r} = (-2\hat{i}+6\hat{j}-10\hat{k})\ m$

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