### Plotting Points on Coordinate AxesOn the coordinate axes provided, plot and label the following points. Draw any guiding lines (or arcs) to give context to the points.#### (a) The Rectangular Point $ R \left( 3, \frac{5\pi}{4}, \frac{3\pi}{4} \right) $.- **Rectangular Coordinates:** Also known as Cartesian coordinates (x, y, z), represent a point in 3D space based on three values.- **Guidelines:** Draw lines from each axis (x, y, z) to illustrate the position of $ R $.#### (b) The Cylindrical Point $ C \left( 3, \frac{5\pi}{4}, \frac{3\pi}{4} \right) $.- **Cylindrical Coordinates:** Represent a point in 3D space with values $(r, \theta, z)$, where: - $ r $: Radial distance from the z-axis, - $ \theta $: Angle from the positive x-axis, - $ z $: Height along the z-axis.- **Guidelines:** Use circular arcs around the z-axis to show the angle $ \theta $ and radial lines from the z-axis to show the distance $ r $.#### (c) The Spherical Point $ S \left( 3, \frac{5\pi}{4}, \frac{3\pi}{4} \right) $.- **Spherical Coordinates:** Represent a point in 3D space with values $(\rho, \theta, \phi)$, where: - $ \rho $: Radial distance from the origin, - $ \theta $: Angle from the positive x-axis, - $ \phi $: Angle from the positive z-axis.- **Guidelines:** Use spherical arcs to represent the angles $ \theta $ and $ \phi $, along with a line from the origin to represent $ \rho $.Please refer to the provided coordinate axes diagram to understand the graphical representation and relationships between the points in different coordinate systems. ### Instruction:In the space below, draw a 3-dimensional rectangular coordinate system. Use this coordinate system for the remainder of this prompt.

The graphical representation of co-ordinate system : Cartesian/Rectangular coordinate system :…

On the coordinate axes above, plot and label the following points. Draw any guiding lines (or arcs) to give context to the points. (a) The rectangular point R (3, , F). (b) The cylindrical point C (3, , F). (c) The spherical point S (3, , 3).

On the coordinate axes above, plot and label the following points. Draw any guiding lines (or arcs) to give context to the points. (a) The rectangular point R (3, , F). (b) The cylindrical point C (3, , F). (c) The spherical point S (3, , 3).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.

Question

### Plotting Points on Coordinate Axes

On the coordinate axes provided, plot and label the following points. Draw any guiding lines (or arcs) to give context to the points.

#### (a) The Rectangular Point $ R \left( 3, \frac{5\pi}{4}, \frac{3\pi}{4} \right) $.

- **Rectangular Coordinates:** Also known as Cartesian coordinates (x, y, z), represent a point in 3D space based on three values.
- **Guidelines:** Draw lines from each axis (x, y, z) to illustrate the position of $ R $.

#### (b) The Cylindrical Point $ C \left( 3, \frac{5\pi}{4}, \frac{3\pi}{4} \right) $.

- **Cylindrical Coordinates:** Represent a point in 3D space with values $(r, \theta, z)$, where:
- $ r $: Radial distance from the z-axis,
- $ \theta $: Angle from the positive x-axis,
- $ z $: Height along the z-axis.
- **Guidelines:** Use circular arcs around the z-axis to show the angle $ \theta $ and radial lines from the z-axis to show the distance $ r $.

#### (c) The Spherical Point $ S \left( 3, \frac{5\pi}{4}, \frac{3\pi}{4} \right) $.

- **Spherical Coordinates:** Represent a point in 3D space with values $(\rho, \theta, \phi)$, where:
- $ \rho $: Radial distance from the origin,
- $ \theta $: Angle from the positive x-axis,
- $ \phi $: Angle from the positive z-axis.
- **Guidelines:** Use spherical arcs to represent the angles $ \theta $ and $ \phi $, along with a line from the origin to represent $ \rho $.

Please refer to the provided coordinate axes diagram to understand the graphical representation and relationships between the points in different coordinate systems.

### Instruction:

In the space below, draw a 3-dimensional rectangular coordinate system. Use this coordinate system for the remainder of this prompt.

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