Tangent of plane to a given surface

[gomes.]

[PLAIN]http://img35.imageshack.us/img35/2033/tangent.jpg

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

but I am 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?

 

[uart]

[PLAIN]http://img35.imageshack.us/img35/2033/tangent.jpg

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

That's not wrong, but it's not such a good answer either. There is a very specific mistake that the student is making here.

but I am 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?

The second one is clearly an attempt at a solution in parametric form (as opposed to the Cartesian for of part "a"). The solution is very nearly correct too, but not quite. Why don't you attempt to derive a correct solution in parametric form and compare it with the given solution.

 

[gomes.]

The second one is clearly an attempt at a solution in parametric form (as opposed to the Cartesian for of part "a"). The solution is very nearly correct too, but not quite. Why don't you attempt to derive a correct solution in parametric form and compare it with the given solution.

Thanks, 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?

 

[uart]

Thanks, 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?

Yeah at a glance just check whether or not the equation is satisfied at the given point (2,3,-1).

Normally with a parametric equation like this I like to keep it in an expanded form like :

(x,y,z) = (1, 0, 12)\, \lambda \, + \, (0, 1, -6) \, \mu \, + \, (2, 3, -1)

In this form it's really obvious that the student has forgotten the last "fixed point" term.