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Found in: Page 57

### Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718

# Find the (a)${\mathbit{x}}$, (b)${\mathbit{y}}$, and (c) ${\mathbit{z}}$components of the sum of the displacements and whose components in meters are ${{\mathbit{c}}}_{{\mathbf{x}}}{\mathbf{=}}{\mathbf{7}}{\mathbf{.}}{\mathbf{4}}{\mathbf{,}}{\mathbf{}}{{\mathbit{c}}}_{{\mathbf{y}}}{\mathbf{=}}{\mathbf{‐}}{\mathbf{3}}{\mathbf{.}}{\mathbf{8}}{\mathbf{,}}{\mathbf{}}{{\mathbit{c}}}_{{\mathbf{z}}}{\mathbf{=}}{\mathbf{‐}}{\mathbf{6}}{\mathbf{.}}{\mathbf{1}}{\mathbf{;}}{\mathbf{}}{{\mathbit{d}}}_{{\mathbf{x}}}{\mathbf{=}}{\mathbf{4}}{\mathbf{.}}{\mathbf{4}}{\mathbf{}}{\mathbf{,}}{\mathbf{}}{{\mathbit{d}}}_{{\mathbf{y}}}{\mathbf{=}}{\mathbf{‐}}{\mathbf{2}}{\mathbf{.}}{\mathbf{0}}{\mathbf{,}}{\mathbf{}}{{\mathbit{d}}}_{{\mathbf{z}}}{\mathbf{=}}{\mathbf{3}}{\mathbf{.}}{\mathbf{3}}$

a) x component of is $c+d\mathrm{is}12\mathrm{m}$

b) y component of is $c+d\mathrm{is}‐5.8\mathrm{m}$

c) z component of is $c+d\mathrm{is}‐2.8\mathrm{m}$

See the step by step solution

## Step 1: To calculate x component in meters

c and d are the displacement vectors. The sum of these vectors gives a resultant. Here the components of the resultant are to be found.

Given are the x, y z, components of the displacements c and d respectively.

${c}_{x}=7.4,\phantom{\rule{0ex}{0ex}}{c}_{y}=-3.8,\phantom{\rule{0ex}{0ex}}{c}_{z}=-6.1,\phantom{\rule{0ex}{0ex}}{d}_{x}=4.4,\phantom{\rule{0ex}{0ex}}{d}_{y}=-2.0,\phantom{\rule{0ex}{0ex}}{d}_{y}=3.3,$

The resultant of sum of displacements is given by

$R=c+d\phantom{\rule{0ex}{0ex}}{R}_{x}={c}_{x}+{d}_{x}\phantom{\rule{0ex}{0ex}}\left(\mathrm{i}\right)\phantom{\rule{0ex}{0ex}}{R}_{y}={c}_{y}+{d}_{y}\phantom{\rule{0ex}{0ex}}\left(\mathrm{ii}\right)\phantom{\rule{0ex}{0ex}}{R}_{z}={c}_{z}+{d}_{z}\phantom{\rule{0ex}{0ex}}\left(\mathrm{iii}\right)$

Substituting the above components in equation (i), the x component of R can be written as

${R}_{x}=7.4+4.4\phantom{\rule{0ex}{0ex}}{R}_{x}=12\mathrm{m}$

## Step 2: To calculate y component in meters

${R}_{y}=-3.8-2.0\phantom{\rule{0ex}{0ex}}{R}_{y}=-5.8\mathrm{m}$

## Step 3: To calculate z component in meters

${R}_{z}=-6.1+3.3\phantom{\rule{0ex}{0ex}}{R}_{z}=-2.8\mathrm{m}$