How Do You Find the Normal to the Parametric Equation r(t) = <acos t, bsin t>?

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SUMMARY

The discussion focuses on finding the normal to the curve defined by the parametric equation r(t) = . It clarifies that a normal is associated with a curve rather than an equation. The key insight provided is that the vector is always normal to the vector <-b, a>, which is crucial for determining the normal at any point on the curve. Additionally, it emphasizes the need for a specific set of coordinates to proceed with the calculation.

PREREQUISITES

  • Understanding of parametric equations
  • Familiarity with vector calculus
  • Knowledge of normal vectors in geometry
  • Basic trigonometric functions and their properties

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  • Study the derivation of normal vectors for parametric curves
  • Learn about the geometric interpretation of vectors in 2D space
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Mathematicians, physics students, and engineers who are working with parametric equations and need to understand the concept of normals in curves.

david90
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r(t) = <acos t , bsin t>
 
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Now, how about you go back, read the question again and the give it exactly.

In the first place an equation doesn't have a normal, a curve does.

If you mean, "find the equation for the normal to the curve given by r(t) = <acos t , bsin t> for any t", then say so.

Heres' a major hint the vector <a, b> is always normal to the vector <-b, a>.
 
In order to have a normal, you need to give us 1 set of coordinates.
 

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