(Solved): Consider the vector field F(x,y,z)=(3z+4y)i+(5z+4x)j+(5y+3x)k. a) Find a function f  ...

Consider the vector field F(x,y,z)=(3z+4y)i+(5z+4x)j+(5y+3x)k.

a) Find a function f such that F=?f and f(0,0,0)=0. 
f(x,y,z)= 

b) Suppose C is any curve from (0,0,0) to (1,1,1). Use part a) to compute the line integral ?CF?dr. 

Consider the vector field \( \mathbf{F}(x, y, z)=(3 z+4 y) \mathbf{i}+(5 z+4 x) \mathbf{j}+(5 y+3 x) \mathbf{k} \) a) Find a function \( f \) such that \( \mathbf{F}=\nabla f \) and \( f(0,0,0)=0 \). \[ f(x, y, z)= \] b) Suppose \( C \) is any curve from \( (0,0,0) \) to \( (1,1,1) \). Use part a) to compute the line integral \( \int_{C} \mathbf{F} \cdot d \mathbf{r} \).