Question

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) ?

Answer 1

it begins with the gradient....

Answer 2

yeah thatl giv u d direction ratios of the tangent plane

Answer 3

4x+2z, 2y, 4z+2x
thats 0, 2, 6

Answer 4

goody goody goody :)

Answer 5

but then how do u get the direction ratios of the normal?

Answer 6

the normal is <0,2,6>; so use the point to calibrate the equation

Answer 7

thats the ratios parallel to the plane

Answer 8

0(x+1)+2(y-1)+6(z-2)=0

Answer 9

thats wrong

Answer 10

those coefficients have to be in the direction of the normal, and not the tangent

Answer 11

can you explain?

Answer 12

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

Answer 13

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

Answer 14

x-x0; y-y0 and z-z0 are the components of the vector on the plane

Answer 15

u get the cross product of <0,2,6> and <-1, 1,2>

Answer 16

thatl give u a vector normal to the plane say <A,B,C>

Answer 17

then use the standard equation

Answer 18

-1,1,2 is a point on the plane right? not a vector parallel to it tho.

Answer 19

yeah

Answer 20

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?

Answer 21

-2(x+1) +6(y-1) +2 (z-2) = 0

Answer 22

-2,6,2 is not the normal to the tangent plane tho. if anything it too is parallel to the plane

Answer 23

arent you suppose to find Fx(X,Y) and Fy(X,Y) use the cross product to find the N?

Answer 24

i told u get the vector product of the direction of the tangent and the point

Answer 25

weve already found the gradient, i suggest we cross that with the point to get a vector normal to the plane

Answer 26

the normal was found by the gradient; isnt the gradient and the normal parallel vectors?

Answer 27

no
the gradient is parallel to the plane

Answer 28

If you found the N and have a point whats the problem?

Answer 29

hmmm.... whats the gradient of 0 = 2x -y +4

Answer 30

just trying to understand concepts :)

Answer 31

<2,-1,0> right?

Answer 32

is that perp or // to y=2x+4 ; z=0?

Answer 33

||

Answer 34

so the vector <2,-1>; whose slope is -1/2 is // with the plne y=2x+2; z=0?

Answer 35

(-1/2)*2=-1.....

Answer 36

u cant define a gradient vector for a line

Answer 37

i didnt; i defined a plane; hence the z=0

Answer 38

fine

Answer 39

bt m saying i think wt i did ws right

Answer 40

Do you guys know about green theorem?

Answer 41

i can tell :)

Answer 42

ive heard f it..nt studied it..

Answer 43

hey sorry..i confirmed..the gradient vector is normal to the surface..rly sorry

Answer 44

if we dot the gradient to a vector parallel to the plane y=2x+4; z=0, we will know if its perp or //

Answer 45

no i confirmed

Answer 46

g=<2,-1,0>
v=<1, 2,0>
--------
2-2+0=0

Answer 47

yes m tellin u its normal to the surface

Answer 48

wt u were doing is right...i feel u alrdy know all this nd ur just testing us out

Answer 49

;) gotta keep entertained ya know lol

Answer 50

mean guy

Answer 51

id give you another medal if i could ;)

Answer 52

wts stopping u??

Answer 53

the only option available to me is the undo lol