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 the vector A from the given expression. In this case, the vector A is given as -9.91i + 11.2j.
2. Recognize that the 'i' component represents the x-direction and the 'j' component represents the y-direction in a Cartesian coordinate system.
3. Extract the x-component from the vector expression. The coefficient of 'i' is the x-component. Here, it is -9.91.
4. Extract the y-component from the vector expression. The coefficient of 'j' is the y-component. Here, it is 11.2.
5. Summarize the components: The x-component of vector A is -9.91, and the y-component of vector A is 11.2.

Key Concepts

Vector Components

Vectors can be broken down into their components along the axes of a coordinate system. In a two-dimensional space, any vector A can be expressed as A = Ai + Aj, where Ai and Aj are the components along the x-axis and y-axis, respectively. This decomposition allows for easier calculations and understanding of the vector's direction and magnitude.

Unit Vectors

Unit vectors are vectors with a magnitude of one, used to indicate direction. In a Cartesian coordinate system, the unit vector in the x-direction is denoted as i, and in the y-direction as j. They serve as the building blocks for expressing any vector in terms of its components, facilitating the representation of vectors in a standardized form.

Coordinate System

A coordinate system provides a framework for defining the position of points in space. In physics, the Cartesian coordinate system is commonly used, where points are defined by their x (horizontal) and y (vertical) coordinates. Understanding this system is essential for analyzing vectors, as it allows for the clear identification of their components and relationships in two-dimensional space.