anonymous
  • anonymous
Find the unit upward normal vector to the ellipsoid 4x^2 + y^2 + z^2 = 9 at the point P(1,2,-1)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
i somehow know the steps to solve this question, but i couldn't understand it completely. any kind soul can explain it to me?\[\nabla f(1,2,-1)=<\frac{\delta f}{\delta x}, \frac{\delta f}{\delta y}, \frac{\delta f}{\delta z}> |_{(1,2,-1)}\]\[\nabla f(1,2,-1)=<8,4,-2>\]right after this im confused on the solution.
anonymous
  • anonymous
|dw:1332754488648:dw|
anonymous
  • anonymous
how does the statement \['\nabla f(1,2,-1) is perpendicular \to f=0 at P(1,2,-1)'\]related to the drawing?

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experimentX
  • experimentX
gradient is defined as the rate of maximum change .... along the maximum change
anonymous
  • anonymous
so the gradient of f at (1,2,-1) is the arrow pointing outwards?
experimentX
  • experimentX
yup ... perpendicular to surface ... but to be honest i don't know the proof.
experimentX
  • experimentX
now you have a vector at that point, i think you can find direction cosines. and given one point you can find the line
anonymous
  • anonymous
ouh, because i'm curious why the solution for upward vector is given as <-8,-4,2> when the gradient of f at the point(1,2,-1) is <8,4,-2>
experimentX
  • experimentX
not sure about that ... though they are parallel and the vector in the figure must be downward ... judging from the coordinate

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