Vector Differentiation with Unit Vectors and Constant Components

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SUMMARY

The discussion focuses on differentiating the vector function v = 2at x + 3bt² y + cz with respect to time to find the acceleration vector a. The correct differentiation yields a = 2a x + 6bt y + 0 z, confirming that the z-component disappears since c is a constant. This conclusion is based on the understanding that a constant component does not contribute to the derivative in vector calculus.

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  • Understanding of vector calculus
  • Familiarity with differentiation of vector functions
  • Knowledge of unit vectors and their notation
  • Concept of constant components in vector fields
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  • Learn about the properties of unit vectors and their applications
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Students studying physics or mathematics, particularly those focusing on vector calculus and its applications in mechanics.

karnten07
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Homework Statement



Differentiate:

v = 2at x + 3bt^2 y + cz

w.r.t time to get a

where x, y and z are unit vecotrs and should have hats above them

Homework Equations





The Attempt at a Solution



I get a = 2a x + 6bt y + z

But I am not sure if that z should completely disappear or not?
 
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If c is a constant, then the derivative will be zero for the z component. (After all, the original specification for v says that the vector field everywhere has a constant z-component and hence a constant inclination to the xy-plane.)
 

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