Let f be a scalar field and F a vector field. State whether each expression is meaningful. If not, explain why. If so, state whether it is a field or a vector field. (a) curl f (b) grad f (c) div F (d) curl(grad f ) (e) grad F (f) grad(div F) (g) div(grad f ) (h) grad(div f ) (i) curl(curl F) (j) div(div F) (k) ( g r a d f ) × ( d i v F ) (l) div(curl(grad f ))
Let f be a scalar field and F a vector field. State whether each expression is meaningful. If not, explain why. If so, state whether it is a field or a vector field. (a) curl f (b) grad f (c) div F (d) curl(grad f ) (e) grad F (f) grad(div F) (g) div(grad f ) (h) grad(div f ) (i) curl(curl F) (j) div(div F) (k) ( g r a d f ) × ( d i v F ) (l) div(curl(grad f ))
Let f be a scalar field and F a vector field. State whether each expression is meaningful. If not, explain why. If so, state whether it is a field or a vector field.
(a) curl f
(b) grad f
(c) div F
(d) curl(grad f)
(e) grad F
(f) grad(div F)
(g) div(grad f)
(h) grad(div f)
(i) curl(curl F)
(j) div(div F)
(k)
(
g
r
a
d
f
)
×
(
d
i
v
F
)
(l) div(curl(grad f))
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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