Consider a coordinate system in which the positive x axis is...

Consider a coordinate system in which the positive $x$ axis is directed upward vertically. What are the positions of a particle (a) $5.0 \mathrm{m}$ directly above the origin and (b) $2.0 \mathrm{m}$ below the origin?

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Key Concepts

Axis Orientation and Sign Conventions

Axis orientation involves defining the direction of each axis, and sign conventions determine whether positions in those directions are positive or negative. In a nonstandard system where the positive x-axis is directed upward vertically, positions above the origin are given positive values, and positions below the origin are represented with negative values.

Coordinate Systems

A coordinate system is a framework defined by perpendicular axes that provide a unique description of every point in a space. It enables us to specify positions with numerical coordinates and is fundamental to geometry, physics, and engineering for accurately modeling arrangements and movements in space.

Position Vectors

A position vector is used to describe the location of a point in space relative to an origin by specifying its coordinates along each axis. It captures both the magnitude and direction, allowing us to clearly identify the point's position within a defined coordinate system using appropriate sign conventions.

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