Determine vector and parametric equations for the z-axis.

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SUMMARY

The vector and parametric equations for the z-axis are defined as x(t) = 0, y(t) = 0, and z(t) = t, where t belongs to the set of real numbers (t ∈ ℝ). This formulation clearly represents the z-axis in a three-dimensional Cartesian coordinate system. The equations indicate that for any value of t, the x and y coordinates remain constant at zero, while the z coordinate varies linearly with t.

PREREQUISITES
  • Understanding of Cartesian coordinate systems
  • Familiarity with vector equations
  • Knowledge of parametric equations
  • Basic grasp of mathematical notation and functions
NEXT STEPS
  • Study vector representation in three-dimensional space
  • Learn about parametric equations and their applications
  • Explore the concept of lines and planes in geometry
  • Investigate the relationship between different coordinate systems
USEFUL FOR

Students in mathematics, physics, or engineering, particularly those studying geometry and vector calculus.

kathialopez
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Determine vector and parametric equations for the z-axis.

HOW DO YOU ANSWER THIS QUESTION?
 
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kathialopez said:
Determine vector and parametric equations for the z-axis.

HOW DO YOU ANSWER THIS QUESTION?

Just a guess since I don't know exactly what definitions you're working from ... but parametric equations for the z-axis would be

x(t) = 0; y(t) = 0; z(t) = t

for [itex]t \in \mathbb{R}[/itex]

Is that what you mean?
 

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