Question

Prove the identity, assuming that the appropriate partial derivatives exist and are continuous. If f is a scalar field and f, g are vector fields, then ff, f.

a) True
b) False

Answer 1

The given statement ff is true for scalar field f and vector fields f and g.

Step-by-step explanation:

The given statement, ff is a true identity for scalar field f and vector fields f and g. To prove this identity, we need to show that the left-hand side (LHS) is equal to the right-hand side (RHS).

LHS = ff = f * f = f2

RHS = f. = f * (f . g) = f * (g . f) = f * (g * f)

We can see that LHS = RHS, so the given identity is true.