91Ó°ÊÓ

In mathematics and physics, the three-dimensional coordinate system is a framework used to pinpoint the location of points in space. It utilizes three numbers to specify points or vectors in 3D space, namely the x, y, and z coordinates. This system is akin to adding an extra dimension to the familiar x-y coordinate plane.

• **x-coordinate**: Measures horizontal position.
• **y-coordinate**: Measures vertical position.
• **z-coordinate**: Measures depth or height.

Using these coordinates, each point in 3D space can be represented as \( (x, y, z) \). Imagine each point as a unique address in a cosmic grid.
The three coordinate planes—xy, xz, and yz—align with these axes to create a three-dimensional map that can help you visualize the location of objects.
The given vector, \( extbf{V}(x, y, z) = [x, 0, 0] \), resides within this framework, sticking to the x-axis as it holds the y and z components at zero.

A Position Vector is a vector that represents the position of a point relative to a particular origin, usually denoted as the coordinate \( (0, 0, 0) \).In the three-dimensional coordinate system, a position vector uses coordinates to indicate this position.
As such, the position vector \( [x, 0, 0] \) maintains a variable horizontal position along the x-axis
but does not elevate or move laterally in the space defined by the y or z values. Think of it as an arrow that lounges along the x-axis, stretching or shrinking as x changes.

Magnitude and direction are key concepts in understanding any vector, including those in three-dimensional fields. They tell us about the vector’s strength and where it points.
This vector essentially captures how far along the x-axis a point is and in which direction. Each point in the field defined by this vector has a magnitude \( |x| \) and direction based on whether x is positive or negative.
This simplifies the vector field into a one-dimensional line along the x-axis with variable magnitude and firm directional guidance.