Explanation Given The vector is of length 3 The vector makes an angle 7 π 4 with the x -axis Key concepts applied: 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 Slope of vector If P 1 ( x 1 , y 1 ) and P 2 ( x 2 , y 2 ) are any two points, the slope of the line joining them P 1 P 2 → are given by, S l o p e = tan θ = y 2 − y 1 x 2 − x 1 , where θ is the angle between the line and the x- axis For a given vector v → = 〈 v x , v y 〉 , v x is the x- component and v y is the y -component, the slope is given by, S l o p e = tan θ = v y v x , where θ is the angle between the line and the x- axis Formulas used: For a two-dimensional vector, the length of the vector is found using the following formula. ‖ a ‖ = a x 2 + a y 2 For a given vector v → = 〈 v x , v y 〉 , v x is the x- component and v y is the y -component, the slope is given by, S l o p e = tan θ = v x v y , where θ is the angle between the line and the x- axis Calculations: Let the vector be a = 〈 a x , a y 〉 Description a = 〈 a x , a y 〉 Step 1...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector spa…

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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, Problem 9CRE

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The vector with the given length and angle with x-axis

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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 vector with the given length and angle with x -axis

Solution Summary: The author explains that any vector can be broken into x- and y-components in a two-dimensional coordinate system.

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The vector with the given length and angle with x-axis

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