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Physics For Scientists & Engineers
Found in: Page 150
Physics For Scientists & Engineers

Physics For Scientists & Engineers

Book edition 9th Edition
Author(s) Raymond A. Serway, John W. Jewett
Pages 1624 pages
ISBN 9781133947271

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Short Answer

A vector points from the origin into the second quadrant of the xy plane. What can you conclude about its components? (a) Both components are positive. (b) The x component is positive, and the y-component is negative. (c) The x-component is negative, and the y-component is positive. (d) Both components are negative. (e) More than one answer is possible.

The correct option is (c).

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Definition of quadrants

A two-dimensional Cartesian system's axes split the plane into four infinite areas called quadrants, each of which is delimited by two half-axes. The coordinates are commonly numbered from 1 to 4 and represented by Roman numerals: I (+, +), || (-, +), III (-, -), and IV (+, -).

Step 2: Explanation for the correct option

Consider the diagram below, which depicts the coordinate system's partition into four quadrants.

Here, x and y are positive for a point in the | quadrant, || the quadrant x is negative, and both x and y are negative for the third quadrant. x is positive and y is negative if the point is in the fourth quadrant.

The issue specifies that the vector extends from the origin to the second quadrant.

The x-component will be negative, whereas the y-component will be positive, as seen in the diagram.

Hence, option (c) is the correct choice.

Step 3: Explanation for option (a)

The x-component will be negative and the y-component will be positive.

So, option (a) is incorrect.

Step 4: Explanation for option (b)

The x-component will be negative and the y-component will be positive.

So, option (b) is incorrect.

Step 5: Explanation for option (d) 

The x-component will be negative and the y-component will be positive.

Quadrant IV denotes (+, -).

So, option (d) is incorrect.

Step 6: Explanation for option (e)

The x-component will be negative and the y-component will be positive.

So, option (e) is incorrect.

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