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

Verified step by step guidance

1. Identify the components of vector A given in the problem. The vector A is expressed in terms of unit vectors i and j, where i represents the x-direction and j represents the y-direction. The vector is given as A = 11.2j - 9.91i.
2. Recognize that the coefficient of i represents the x-component of the vector, and the coefficient of j represents the y-component of the vector.
3. Extract the x-component from the vector A. Since the vector is given as A = 11.2j - 9.91i, the x-component is -9.91.
4. Extract the y-component from the vector A. The y-component is given by the coefficient of j, which is 11.2.
5. Conclude that the x-component of vector A is -9.91 and the y-component is 11.2. These components can be used in further calculations or to understand the direction and magnitude of the vector in a coordinate system.

Key Concepts

Vector Components

Vector components are the projections of a vector along the axes of a coordinate system. In a two-dimensional Cartesian system, any vector can be broken down into x- and y-components, 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 in a coordinate system. In Cartesian coordinates, the unit vectors i and j represent the x-axis and y-axis directions, respectively. They are essential for expressing vectors in terms of their components.

Vector Notation

Vector notation involves expressing vectors using their components and unit vectors. For example, a vector A can be written as A = Ax i + Ay j, where Ax and Ay are the magnitudes of the vector's components along the x and y axes, respectively. This notation helps in visualizing and calculating vector operations.