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V x (A(x, y, z)▼B(x, y, z)) = VB × VA where A and B are differentiable scalar functions of x, y, and z. You can look in a table of vector calculus identities and check easily enough whether my assertion is true. But don't just cite the table. Instead, do one (1) of the following: • Derive the identity for arbitrary functions A and B (thus proving my assertion true). • Derive some different identity for V x (AVB) (thus proving my assertion false). • Give me functions A and B for which my assertion does not hold. You don't have to do more than one of those things. Just one (1) will suffice.

V x (A(x, y, z)▼B(x, y, z)) = VB × VA where A and B are differentiable scalar functions of x, y, and z. You can look in a table of vector calculus identities and check easily enough whether my assertion is true. But don't just cite the table. Instead, do one (1) of the following: • Derive the identity for arbitrary functions A and B (thus proving my assertion true). • Derive some different identity for V x (AVB) (thus proving my assertion false). • Give me functions A and B for which my assertion does not hold. You don't have to do more than one of those things. Just one (1) will suffice.

Advanced Engineering Mathematics
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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V x (A(x, y, z)VB(x,y, z)) = VB × VA where A and B are differentiable scalar functions of x, y, and z. You can look in a table of vector calculus identities and check easily enough whether my assertion is true. But don't just cite the table. Instead, do one (1) of the following: • Derive the identity for arbitrary functions A and B (thus proving my assertion true). • Derive some different identity for V x (AVB) (thus proving my assertion false). • Give me functions A and B for which my assertion does not hold. You don't have to do more than one of those things. Just one (1) will suffice.
Transcribed Image Text:V x (A(x, y, z)VB(x,y, z)) = VB × VA where A and B are differentiable scalar functions of x, y, and z. You can look in a table of vector calculus identities and check easily enough whether my assertion is true. But don't just cite the table. Instead, do one (1) of the following: • Derive the identity for arbitrary functions A and B (thus proving my assertion true). • Derive some different identity for V x (AVB) (thus proving my assertion false). • Give me functions A and B for which my assertion does not hold. You don't have to do more than one of those things. Just one (1) will suffice.
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