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Math Help - equation of tangent plane to a surface

  1. #1
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    equation of tangent plane to a surface



    I managed to do the first part okay ---- said some stuff about 3x^2 and y^2 term, its not linear etc..

    but Im stuck in the part in red. Is it supposed to be something about a normal vector? How do i know what is wrong? and what mistake was made?

    I calculated the equation of the tangent plane and it is: z=12(x−2)−6(y−3)-1

    and the tangent plane has normal vector (12,-6,-1) at (2,3) ----- could it be something to do with the part circled in red?
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  2. #2
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    Yes, "Answer 1" is clearly wrong because it is not linear and so not the equation of any plan.

    Now, "Answer 2" is a plane- it is linear parametric equations with two parameters.
    The simplest answer is that when x= 2 and y= 3, z= 8- 9= -1. But there are no values of \lambda and \mu that make (\lambda, \mu, 12\lambda- 6\mu)= (2, 3, -1). It should be easy to see that and that means that the given plane does NOT include that point.
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  3. #3
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    Thanks, and for part 2 --- im meant to say what mistake the student made (b) and how to fix it (c). How would i find the "precise" mistake the student made, and how can i correct "answer 2"?
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  4. #4
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    for the 2nd part, i got (lamba, mu, 12lamba-6mu-7)

    So can i say the student forgot to put/calculate in the -7 in the parametric form? At a glance, how would i know the student got it wrong? Because he didnt put in the -7?
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  5. #5
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    Yes, that's good. As I said before, the simplest way to see that the second answer was wrong was to note that it did not include the point (2, 3, -1). As for "what mistake the student made", there could have been many! But the most likely was just that he forgot the "-7".
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