Find two unit vectors that are normal to the given plan and the point. sqrt((z+x)/(y-1)) = z^2 and the point is P(3, 5, 1).
I took partial derivatives and got fx = 1, fy = -z^4 and fz = 1 - 4z^3y + 4z^3 but now I'm stuck.

Question

Find two unit vectors that are normal to the given plan and the point.  sqrt((z+x)/(y-1)) = z^2   and the point is P(3, 5, 1).
I took partial derivatives and got fx = 1, fy = -z^4 and fz = 1 - 4z^3y + 4z^3 but now I'm stuck.

amistre64 · Answer

the gradient of a function defines the normal

amistre64 · Answer

gradF = <fx, fy, fz>

anonymous · Answer

Should I substitute the coordinates of the point into the partial derivatives?

amistre64 · Answer

yes, the partials are the equations for the normal components; after wards

amistre64 · Answer

once you define the vector; divide it by its magnitude to get it to unit length

anonymous · Answer

So for the gradient I get i - j - 15k

amistre64 · Answer

should i trust you on that?  :)

now divide it by its magnitude to unit it out

amistre64 · Answer

once you determine that unit normal; negate its components and you got the normal again in the opposite direction

anonymous · Answer

OK--thank you for your help!

amistre64 · Answer

yw

anonymous · Answer

This was the problem taht I had and when I solved it I got i - j -15k, the book has i - j -19k ... I do not know why? Their magnatude was also something different from what I got. For magnatude I used ||a|| and divided by that number to get the unit vector. Can anyone figure out why the book has a different value for k??