Ch 01: Units, Physical Quantities & Vectors

Young & Freedman Calc - University Physics 15th Edition

Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook

Young & Freedman Calc 15th Edition

Ch 01: Units, Physical Quantities & Vectors

Problem 34b

Chapter 1, Problem 34b

In each case, find the x- and y- components of vector A: A = 11.2j - 9.91i

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Understand that vector A is given in terms of unit vectors i and j, where i represents the x-direction and j represents the y-direction.

Identify the components of vector A from the given expression: A = 11.2j - 9.91i.

Recognize that the coefficient of i represents the x-component of the vector, and the coefficient of j represents the y-component.

Extract the x-component of vector A, which is -9.91, since it is associated with the i unit vector.

Extract the y-component of vector A, which is 11.2, since it is associated with the j unit vector.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Vector Components

Vector components are the projections of a vector along the axes of a coordinate system. In a two-dimensional space, any vector can be broken down into its x-component and y-component, which represent the vector's influence in the horizontal and vertical directions, respectively.

Unit Vectors

Unit vectors are vectors with a magnitude of one, used to indicate direction along the axes in a coordinate system. In Cartesian coordinates, the unit vectors i and j represent the x-axis and y-axis directions, respectively, allowing vectors to be expressed in terms of these components.

Vector Notation

Vector notation is a mathematical representation of vectors using symbols and numbers. In physics, vectors are often expressed in terms of their components using unit vectors, such as A = 11.2j - 9.91i, where the coefficients of i and j indicate the magnitude of the vector's components along the x and y axes.

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