Question

Write the equation of a plane : \[\vec r(u,v) =2\sin(u)\hat i + 3\cos(u)\hat j +v\hat k\] \(0\le v\le 2\)

Answer 1

some vector stoof

Answer 2

r_u X r_v

Answer 3

\[P_0 = (2,3,0)\]

Answer 4

will give yu normal line <a,b,c>
d=ax+by+cz

Answer 5

plug po in and see what d has to be

Answer 6

I can do this but I can't really visualize this haha.

Answer 7

basicalllyy

Answer 8

Uhh... vector a.... or \(\vec r_u = <\cos(u) ~ , ~ -\sin(u)~,~0>\)

Answer 9

hm

Answer 10

\[\vec b = <0,0,1>\]

Answer 11

you're trying to find the tangent plane of given surface at given point ?

Answer 12

Im so lazy rn.

Answer 13

Yeah.

Answer 14

i know what we find can be the tangent pane, but can u say this whole thing iss a plane

Answer 15

that whole thing looks like a cylinder to me

Answer 16

Dan this is the first and last time you'll hear this, can you draw it out please?

Answer 17

it is aligning in z axis

Answer 18

its an elliptic cylinder in u,v

Answer 19

\[a \times b =\]