Question

12. –/3 points My Notes
Question Part
Points
Submissions Used
1 2 3
–/1 –/1 –/1
0/1 0/1 0/1
Total
–/3

Determine if the statements below are true or false.

(a) If
F · dA
S
= 12
and S is a flat disk of area 4π, then
divF =
3
π
.
True False

(b) If
F
is a vector field in 3-space, then
grad(divF) = 0 i  + 0 j  + 0 k 

True False

(c) If S is the unit sphere oriented outward and
F
is a vector field satisfying
F · dA
S
= 0
, then
divF = 0
at all points inside S.
True False

Answer 1

@ganeshie8

Answer 2

here's a picture better

Answer 3

I pretty sure C is false but I don't know about "a" and "b"

Answer 4

@ganeshie8 can you see the picture?

Answer 5

for b :
consdier F = <x^2, 0, 0>
div(F) = 2x
grad(div F) = <2, 0,0>

so clearly b has to be false, yes ?

Answer 6

so only when vector field is <0, 0, 0 > meaning never

Answer 7

meaning, it need not be <0,0,0> always

Answer 8

the grad(div F) could be any other vector different from zero vector

Answer 9

oh ok

Answer 10

so what about A @ganeshie8

Answer 11

I only have 1 minute

Answer 12

I guess false and got it right

Answer 13

Oh sorry i was still thinking :o

Answer 14

a : false
b : false
c : ?

Answer 15

C is also false