Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Vector Graphing Exercise
**1. Graph the vectors:**
**a) \(-3, 0, 1\)**
In this graph, the vector \(-3, 0, 1\) is visualized in a 3-dimensional coordinate system with x, y, and z axes. The vector starts at the origin (0, 0, 0) and points to the coordinates \(-3\) on the x-axis, \(0\) on the y-axis, and \(1\) on the z-axis. The grid lines provide a reference to show the position of the vector in the coordinate plane.
**b) \(0, 5, 0\)**
In this graph, the vector \(0, 5, 0\) is visualized in a similar 3-dimensional coordinate system. The vector starts at the origin (0, 0, 0) and points to the coordinates \(0\) on the x-axis, \(5\) on the y-axis, and \(0\) on the z-axis. Again, the grid lines serve as a reference to accurately place the vector in the coordinate plane.
### Diagrams Explanation:
- Each diagram consists of a 3-dimensional coordinate plane featuring the x, y, and z axes.
- Vectors are represented by arrows starting from the origin and pointing towards the given coordinates.
- Grids are used to help visualize the spatial relationships and positions of the vectors in the 3-dimensional space.
- The vector in part a) extends from the origin to \(-3\) on the x-axis and \(1\) on the z-axis.
- The vector in part b) extends from the origin to \(5\) on the y-axis.
These visual aids help in comprehending the direction and magnitude of vectors in a 3-dimensional space.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feebaec1b-ee06-4b3e-9e54-22422c96ad5b%2F98bf668c-5d9d-4078-bef2-35d4e59bc02e%2Fa4nqesu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Vector Graphing Exercise
**1. Graph the vectors:**
**a) \(-3, 0, 1\)**
In this graph, the vector \(-3, 0, 1\) is visualized in a 3-dimensional coordinate system with x, y, and z axes. The vector starts at the origin (0, 0, 0) and points to the coordinates \(-3\) on the x-axis, \(0\) on the y-axis, and \(1\) on the z-axis. The grid lines provide a reference to show the position of the vector in the coordinate plane.
**b) \(0, 5, 0\)**
In this graph, the vector \(0, 5, 0\) is visualized in a similar 3-dimensional coordinate system. The vector starts at the origin (0, 0, 0) and points to the coordinates \(0\) on the x-axis, \(5\) on the y-axis, and \(0\) on the z-axis. Again, the grid lines serve as a reference to accurately place the vector in the coordinate plane.
### Diagrams Explanation:
- Each diagram consists of a 3-dimensional coordinate plane featuring the x, y, and z axes.
- Vectors are represented by arrows starting from the origin and pointing towards the given coordinates.
- Grids are used to help visualize the spatial relationships and positions of the vectors in the 3-dimensional space.
- The vector in part a) extends from the origin to \(-3\) on the x-axis and \(1\) on the z-axis.
- The vector in part b) extends from the origin to \(5\) on the y-axis.
These visual aids help in comprehending the direction and magnitude of vectors in a 3-dimensional space.
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