1. Assume that F(x,y, z) is a 3D vector field and f (x,y,z) is a function of 3 variables. For each o the quantities below, determine if the expression is nonsense, a vector, or a scalar. (Something like ( 2,3 ) × ( 0,1 ) would be an example of "nonsense," since it is not possible to take the cross-product of two-dimensional vectors.) F(x, y,z) Nonsense Scalar Vector f(x, y, z) Scalar Nonsense Vector Vf(x,y, z) Nonsense Vector Scalar div F (x,y, z) Scalar Nonsense Vector div f (x,y,z) Nonsense Vector Scalar curl F(x,y,z) Nonsense Vector Scalar div curl F (x, y,z) Nonsense Vector Scalar curl div F (x,y,z) Scalar Nonsense Vector curl Vf(x, y, z) Nonsense Scalar Vector
1. Assume that F(x,y, z) is a 3D vector field and f (x,y,z) is a function of 3 variables. For each o the quantities below, determine if the expression is nonsense, a vector, or a scalar. (Something like ( 2,3 ) × ( 0,1 ) would be an example of "nonsense," since it is not possible to take the cross-product of two-dimensional vectors.) F(x, y,z) Nonsense Scalar Vector f(x, y, z) Scalar Nonsense Vector Vf(x,y, z) Nonsense Vector Scalar div F (x,y, z) Scalar Nonsense Vector div f (x,y,z) Nonsense Vector Scalar curl F(x,y,z) Nonsense Vector Scalar div curl F (x, y,z) Nonsense Vector Scalar curl div F (x,y,z) Scalar Nonsense Vector curl Vf(x, y, z) Nonsense Scalar Vector
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. Assume that F(x, y, z) is a 3D vector field and f(x, y, z) is a function of 3 variables. For each of
the quantities below, determine if the expression is nonsense, a vector, or a scalar.
(Something like ( 2,3 ) × ( 0,1 ) would be an example of “nonsense," since it is not possible to
take the cross-product of two-dimensional vectors.)
F(x,y, z)
Nonsense
Vector
Scalar
f(x, y, z)
Scalar
Nonsense
Vector
Vf (x, y, z)
Nonsense
Vector
Scalar
div F (x, y, z)
Nonsense
Vector
Scalar
div f (x,y, z)
Scalar
Nonsense
Vector
curl F(x, y, z)
Nonsense
Vector
Scalar
div curl F(x, y, z)
Nonsense
Vector
Scalar
curl div F (x, y, z)
Nonsense
Vector
Scalar
curl Vf (x,y,z)
Nonsense
Scalar
Vector
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