Question

What is the divergence of the vector field
F = 3x2î + 5xy2ſ + xy23 Ř
at the point (1,2,3)
2​

Answer 1

Answer:

(2x−3) is a factor of p(x)=2x

3

−9x

2

+x+K,

If (2x−3)=0,x=

2

3

If (2x−3) is a factor of p(x) then p(

2

3

)=0

p(x)=2x

3

−9x

2

+x+K,

⇒p(

2

3

)=2(

2

3

)−9(

2

3

)+

2

3

+K=0

⇒2(

8

27

)−9(

4

9

)+

2

3

+K=0

⇒(

4

27

−

4

81

+

2

3

+K=0)×4

27−81+6+4K=0

−48+4K=0

4K=48

So K=12