Vector function F(x,y,z) = (e^3yz) i + (e^2xz) j + ( e^xy ) k. How would you calculate curl F at (1,1,1)?

Question

these are possible answers that the response can be checked with....


a. (3e^3 - 2e^2)i + (e - 3e^3)j + (2e^2 - e)k
b. (3e^3 - e)i + (2e^2 - 3e^3)j + (e - 2e^2)k
c. (e - 2e^2)i + (3e^3 - e)j + (2e^2 - 3e^3)k
d. (2e^2 - e)i + (3e^3 - 2e^2)j + (e - 3e^3)k
e. (2e^2 - 3e^3)i + (e - 2e^2)j + (3e^3 - e)k
f. (e - 3e^3)i + (2e^2 - e)j + (3e^3 - 2e^2)k
g. none of these

Answer 1

Take the determinant of the following matrix:

row 1( i j k)
row 2( d/dx d/dy d/dz )
row 3( Fx Fy Fz )

Those are partial derivatives in the second row.

Once you have found the determinant of that matrix, just plug in (1,1,1) and you will get choice c as your answer

Answer 2

There is a vector operator called "nabla"
the symbol is an inverted triangle(I´ll useD)


D= d/dx i+d/dy j+d/dz k
if your vector is
V= Pi+Qj+Rk ,curl V is the vector product of D and V