Consider the given vector field. f(x, y, z) = 8xyezi + yzexk (a) find the curl of the vector field. curl f = $$zexi+(8xyez−yzex)j−8xezk correct: your answer is correct. (b) find the divergence of the vector field. div f = $$8yez+yex correct: your answer is correct.

(a)

(b)

Step-by-step explanation:

We are given a vector function f(x,y,z) as:

where,

(a)

Hence, the curl f is calculated as:

Hence, we have:

Hence,

Hence,

(b)

Divergence f is calculated as:

true? is that what you're asking or do you mean something else?

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!