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amistre64

  • 5 years ago

What is the equation of the tangent plane to the function: 2x^2 +y^2 +2z^2 +2xz =7. At the point (-1,1,2) ?

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  1. amistre64
    • 5 years ago
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    it begins with the gradient....

  2. anonymous
    • 5 years ago
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    yeah thatl giv u d direction ratios of the tangent plane

  3. anonymous
    • 5 years ago
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    4x+2z, 2y, 4z+2x thats 0, 2, 6

  4. amistre64
    • 5 years ago
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    goody goody goody :)

  5. anonymous
    • 5 years ago
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    but then how do u get the direction ratios of the normal?

  6. amistre64
    • 5 years ago
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    the normal is <0,2,6>; so use the point to calibrate the equation

  7. anonymous
    • 5 years ago
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    thats the ratios parallel to the plane

  8. amistre64
    • 5 years ago
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    0(x+1)+2(y-1)+6(z-2)=0

  9. anonymous
    • 5 years ago
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    thats wrong

  10. anonymous
    • 5 years ago
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    those coefficients have to be in the direction of the normal, and not the tangent

  11. amistre64
    • 5 years ago
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    can you explain?

  12. amistre64
    • 5 years ago
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    n=<a,b,c>; P=(x0,y0,z0) equation of the plane: a(x-x0)+b(y-y0)+c(z-z0)=0 is the way the textbook tells me it

  13. anonymous
    • 5 years ago
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    ur using the standard eqn of a plane passing through a given pt a,b,c A(x-a) + B(x-b) +C(x-c)=0 where A,B,C are direction ratios of the NORMAL

  14. amistre64
    • 5 years ago
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    x-x0; y-y0 and z-z0 are the components of the vector on the plane

  15. anonymous
    • 5 years ago
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    u get the cross product of <0,2,6> and <-1, 1,2>

  16. anonymous
    • 5 years ago
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    thatl give u a vector normal to the plane say <A,B,C>

  17. anonymous
    • 5 years ago
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    then use the standard equation

  18. amistre64
    • 5 years ago
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    -1,1,2 is a point on the plane right? not a vector parallel to it tho.

  19. anonymous
    • 5 years ago
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    yeah

  20. amistre64
    • 5 years ago
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    the vector that is parallel to the plane is (x-x0,y-y0,z-z0) where P(x0,y0,z0) is on the plane right?

  21. anonymous
    • 5 years ago
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    -2(x+1) +6(y-1) +2 (z-2) = 0

  22. amistre64
    • 5 years ago
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    -2,6,2 is not the normal to the tangent plane tho. if anything it too is parallel to the plane

  23. anonymous
    • 5 years ago
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    arent you suppose to find Fx(X,Y) and Fy(X,Y) use the cross product to find the N?

  24. anonymous
    • 5 years ago
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    i told u get the vector product of the direction of the tangent and the point

  25. anonymous
    • 5 years ago
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    weve already found the gradient, i suggest we cross that with the point to get a vector normal to the plane

  26. amistre64
    • 5 years ago
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    the normal was found by the gradient; isnt the gradient and the normal parallel vectors?

  27. anonymous
    • 5 years ago
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    no the gradient is parallel to the plane

  28. anonymous
    • 5 years ago
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    If you found the N and have a point whats the problem?

  29. amistre64
    • 5 years ago
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    hmmm.... whats the gradient of 0 = 2x -y +4

  30. amistre64
    • 5 years ago
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    just trying to understand concepts :)

  31. amistre64
    • 5 years ago
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    <2,-1,0> right?

  32. amistre64
    • 5 years ago
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    is that perp or // to y=2x+4 ; z=0?

  33. anonymous
    • 5 years ago
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    ||

  34. amistre64
    • 5 years ago
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    so the vector <2,-1>; whose slope is -1/2 is // with the plne y=2x+2; z=0?

  35. amistre64
    • 5 years ago
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    (-1/2)*2=-1.....

  36. anonymous
    • 5 years ago
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    u cant define a gradient vector for a line

  37. amistre64
    • 5 years ago
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    i didnt; i defined a plane; hence the z=0

  38. anonymous
    • 5 years ago
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    fine

  39. anonymous
    • 5 years ago
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    bt m saying i think wt i did ws right

  40. anonymous
    • 5 years ago
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    Do you guys know about green theorem?

  41. amistre64
    • 5 years ago
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    i can tell :)

  42. anonymous
    • 5 years ago
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    ive heard f it..nt studied it..

  43. anonymous
    • 5 years ago
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    hey sorry..i confirmed..the gradient vector is normal to the surface..rly sorry

  44. amistre64
    • 5 years ago
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    if we dot the gradient to a vector parallel to the plane y=2x+4; z=0, we will know if its perp or //

  45. anonymous
    • 5 years ago
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    no i confirmed

  46. amistre64
    • 5 years ago
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    g=<2,-1,0> v=<1, 2,0> -------- 2-2+0=0

  47. anonymous
    • 5 years ago
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    yes m tellin u its normal to the surface

  48. anonymous
    • 5 years ago
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    wt u were doing is right...i feel u alrdy know all this nd ur just testing us out

  49. amistre64
    • 5 years ago
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    ;) gotta keep entertained ya know lol

  50. anonymous
    • 5 years ago
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    mean guy

  51. amistre64
    • 5 years ago
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    id give you another medal if i could ;)

  52. anonymous
    • 5 years ago
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    wts stopping u??

  53. amistre64
    • 5 years ago
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    the only option available to me is the undo lol

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