Explanation Given: The following points, P 1 = ( 1 , − 3 , 5 ) P 2 = ( − 1 , 3 , 5 ) Key concept applied: In three-dimensional rectangular coordinate system , we specify the location of a point by first giving its x coordinate, then the y coordinate and then the z coordinate. Thus, every point on the plane can be identified by a set of three numbers ( x , y, z ), called its coordinates . The projection of a point in three-dimensions can be made on the xy- plane. In the xy- plane The axes naturally divide the plane up into quarters. We call these quadrants , and number them from one to four. Converting from rectangular to polar coordinates When we know a point in Cartesian Coordinates ( x, y ) and we want it in Polar Coordinates ( r, θ ) we can use the following formulas. r = x 2 + y 2 θ = tan − 1 y x Calculations: Description Step 1. Find the projection of the point P 1 = ( 1 , − 3 , 5 ) on the xy- plane. Find θ using the formula θ = tan − 1 y x The projection of the point P 1 = ( 1 , − 3 , 5 ) on the xy- plane is ( 1 , − 3 ) ...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

Chapter 13.7, Problem 72E

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The quadrants of the xy-plane in which the projections of the given points will lie

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Chapter 13.7, Problem 71E

Chapter 13.7, Problem 73E

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Chapter 13 Solutions

Calculus - Standalone book

Ch. 13.1 - Prob. 1PQ Ch. 13.1 - Prob. 2PQ Ch. 13.1 - Prob. 3PQ Ch. 13.1 - Prob. 4PQ Ch. 13.1 - Prob. 5PQ Ch. 13.1 - Prob. 6PQ Ch. 13.1 - Prob. 1E Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E

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The quadrants of the xy -plane in which the projections of the given points will lie

Solution Summary: The author explains how the projection of a point in three-dimensions can be made on the xy-plane.

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The quadrants of the xy-plane in which the projections of the given points will lie

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Chapter 13 Solutions