Explanation Given: The following points, P = ( 1 , 4 ) Q = ( − 3 , 5 ) Key concepts applied: Vector joining two points If P 1 ( x 1 , y 1 ) and P 2 ( x 2 , y 2 ) are any two points, then the vector joining P 1 and P 2 is given by, P 1 P 2 → = O P 2 → − O P 1 → Components of a vector In a two-dimensional coordinate system , any vector can be broken into x- component and y -component. For example, in the vector, v → = 〈 v x , v y 〉 , v x is the x- component and v y is the y -component. Consider a vector r written as x i + y j . This form of the vector is called its component form. Here, x and y are called as the scalar components of the vector, and x i , and y j and are called the vector components of the vector along the respective axes. Sometimes x and y are also termed as the rectangular components. Length of a vector The magnitude of a vector is the length of the vector. The length of a vector in Cartesian coordinates is the square root of the sum of the squares of its coordinates. For a two-dimensional vector, the length of the vector is found using the following formula. ‖ a ‖ = a x 2 + a y 2 Formula used: Vector joining two points If P 1 ( x 1 , y 1 ) and P 2 ( x 2 , y 2 ) are any two points, then the vector joining P 1 and P 2 is given by, P 1 P 2 → = O P 2 → − O P 1 → Components of a vector In a two-dimensional coordinate system, any vector can be broken into x- component and y -component. For example, in the vector, v → = 〈 v x , v y 〉 , v x is the x- component and v y is the y -component...

4th Edition

ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Question

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 12, Problem 7CRE

To determine

To calculate:

The components and length of the given vector.

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Chapter 12, Problem 6CRE

Chapter 12, Problem 8CRE

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Chapter 12 Solutions

Calculus: Early Transcendentals

Ch. 12.1 - Prob. 1PQ Ch. 12.1 - Prob. 2PQ Ch. 12.1 - Prob. 3PQ Ch. 12.1 - Prob. 4PQ Ch. 12.1 - Prob. 5PQ Ch. 12.1 - Prob. 6PQ Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E

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The components and length of the given vector .

To calculate: The components and length of the given vector.

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Chapter 12 Solutions

To calculate:

The components and length of the given vector.