Who here likes multi-variable Calculus?

Find the two points on the surface 3x^2+4y^2+3z^2=1 at which the tangent plane is parallel to the plane x-3y+2z=-1

Question

Who here likes multi-variable Calculus? 

Find the two points on the surface 3x^2+4y^2+3z^2=1 at which the tangent plane is parallel to the plane x-3y+2z=-1

ganeshie8 · Answer

gradiant gives the normal vector to the tangent plane

ganeshie8 · Answer

so, start by finding the gradient vector

ganeshie8 · Answer

and see when it is parallel to the given plane

ganeshie8 · Answer

gradiant of given surface : $\left<6x, 8y ,6z\right>$

ganeshie8 · Answer

since this vector is normal to the tangent plane, u need to find the condition for this vector to be parallel to the normal of given plane

anonymous · Answer

okay, that seems like a better method. In my notes I had written down that the normal to the tangent plane had the vector equation n=<dz/dx , dy/dx , -1> so I tried with that a few times to no avail. I'll give it a shot with the gradient instead. Any idea what I was doing though?

ganeshie8 · Answer

yes, that works too...

ganeshie8 · Answer

oly problem wid that method is, u need to solve "z", which im sure u dont wana do :)

anonymous · Answer

hmm.. possibly algebra errors then...

ganeshie8 · Answer

http://www.wolframalpha.com/input/?i=solve+%3C6x%2C+8y%2C+6z%3E+cross+%3C1%2C-3%2C2%3E+%3D+0

ganeshie8 · Answer

just put random values for "x", 
u wil get "y" and "z" values

ganeshie8 · Answer

see if that looks okay...

anonymous · Answer

oh wolfram. you always are the best... and yep! i think i've got it now. Cheers!

ganeshie8 · Answer

np :) you're the bestie !!