Book edition 9th Edition

Author(s) Raymond A. Serway, John W. Jewett

Pages 1624 pages

ISBN 9781133947271

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Short Answer

Given the vectors $\vec{A} = 2.00 \hat{i} + 6.00 \hat{j}$ and $\vec{B} = 3.00 \hat{i} - 2.00 \hat{j}$ , (a) draw the vector sum $\vec{C} = \vec{A} + \vec{B}$ and the vector difference $\vec{D} = \vec{A} - \vec{B} .$ (b) Calculate $\vec{C}$ and $\vec{D}$ , in terms of unit vectors. (c) Calculate $\vec{C}$ and $\vec{D}$ in terms of polar coordinates, with angles measured with respect to the positive x axis.

a) The graph is drawn below.

b) $\vec{C} = 5 \hat{i} + 4 \hat{j} a n d \vec{D} = - 1 \hat{i} + 8 \hat{j}$

c) $| \vec{D} | = 8.06 a n d θ_{D} = 97.1 °$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Define vector, polar coordinates, and unit vector

A quantity that has both magnitude and direction is called a vector. It's usually represented by an arrow with the same direction as the amount and a length proportionate to the magnitude of the quantity.
A vector does not have a position, even though it has magnitude and direction.
Polar coordinates are two integers that indicate the position of a point on a plane: a distance and an angle.
A unit vector is a vector with the same magnitude as the magnitude of the magnitude.

Step 2: (a) Plot the graph of the vector sum and vector difference

The vector sum $\vec{C} = \vec{A} + \vec{B}$ and the vector difference $\vec{D} = \vec{A} - \vec{B} .$

Step 3: (b) Determine the vector total and difference

We just add or subtract the corresponding components to determine the vector total or difference.

$\vec{C} = \vec{A} + \vec{B} = (2 \hat{i} + 6 \hat{j}) + (3 \hat{i} - 2 \hat{j}) = 5 \hat{i} + 4 \hat{j} \vec{D} = \vec{A} - \vec{B} = (2 \hat{i} + 6 \hat{j}) - (3 \hat{i} - 2 \hat{j}) = - 1 \hat{i} + 8 \hat{j}$

Step 4: (c) Determine the polar coordinates

In order to find $\vec{C}$ and $\vec{D}$ in polar coordinates, we must first determine their magnitudes and angles with the +x-axis.

$| \vec{C} | = \sqrt{5^{2} + 4^{2}} = 6.40 θ_{c} = t a n^{- 1} \frac{4}{5} = 38.7 ° | \vec{D} | = \sqrt{{(- 1)}^{2} + 8^{2}} = 8.06$

$θ_{D} = t a n^{- 1} \frac{8}{- 1} = - 82.9 + 180 ° = 97.1 ° H e n c e, | \vec{D} | = 8.06 a n d θ_{D} = 97.1 °$

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Physics For Scientists & Engineers

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Short Answer

Step by Step Solution

Step 1: Define vector, polar coordinates, and unit vector

Step 2: (a) Plot the graph of the vector sum and vector difference

Step 3: (b) Determine the vector total and difference

Step 4: (c) Determine the polar coordinates

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Physics For Scientists & Engineers

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Short Answer

Step by Step Solution

Step 1: Define vector, polar coordinates, and unit vector

Step 2: (a) Plot the graph of the vector sum and vector difference

Step 3: (b) Determine the vector total and difference

Step 4: (c) Determine the polar coordinates

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