Question

Compute the flux of the vector field, F, through the surface, S.
vector F= 7xi + yj + zk and S is the part of the surface z + 4x + 2y = 12 in the first octant oriented upward

Answer 1

help me please @ganeshie8 :)

Answer 2

help me @perl

Answer 3

@eliassaab can you help me out professor

Answer 4

have you sketched the plane on an x, y, z coordinate system?

Answer 5

yea

Answer 6

@dan815 can you help me please

Answer 7

The normal vector to the plane z + 4 x + 2 y = 12 is n = {4, 2, 1} and the field is
{7 x, y ,z}
First compute their dot product

Answer 8

The dot product
{4, 2, 1} . {7 x, y ,z}= 28x+ 2y + z
You have to integrate (as surface integral) 28 x + 2 y + z over the
part of the plane in the first octant

Answer 9

Knowing that z = 12 - 4 x -2y, then
28 x + 2 y + z= 28 x + 2 y + 12 - 4 x -2y= 12 + 24 x
The length of the normal vector n \(\sqrt{21}\)
Can you finish it now?

Answer 10

The last step is to compute this integral
\[
\int_0^3 \left(\int_0^{6-2 x} \sqrt{21}
(24 x+12) \, dy\right) \, dx=324
\sqrt{21}
\]

Answer 11

that's the same thing I got but it's wrong

Answer 12

@eliassaab

Answer 13

I think it is right, unless you did not state the problem correctly

Answer 14

see :/

Answer 15

The problem can be wrongly programmed

Answer 16

how would I use this formula on this problem

Answer 17

@eliassaab

Answer 18

the answer is just 324 don't need the length. I used the flux formula

Answer 19

@eliassaab