I need the answer as soon as possible Consider the scalar field, ø(r), and the vector fields ü(r) and ū(r). Using indexnotation, prove the following identities:(a) V. (ø T) = ū . Vo + ¢ỹ · õ.(b) V× (ø t) = ¢ỹ ×ð – i x Vø.(c) V·(ū× í) = · ỹ × ū – ū · ỹ x ū.(d) V× (ũ x ī) = ở . ỹũ – ū ỹ ·ũ +ūÿ·¯ – ủ · ỹ ở.V •Introduce parentheses on the right-hand side of these equations to indicate the orderof operations and improve legibility by identifying scalar and vector quantities.

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Consider the scalar field, (F), and the vector fields ü(r) and ü(F). Using index notation, prove the following identities: (a) V. (ø T) = ū . Vø + ¢ỹ ·õ. (b) V× (ø i) = pỹ ×ũ – ở × Vø. (c) V·(ũ x ū) = · ỹ × ũ – - Ÿ × ū. (d) V × (ũ x ĩ) = . ỹ ū – ūỹ · ū +ūỷ •ỡ – ủ · ỹ ū. Introduce parentheses on the right-hand side of these equations to indicate the order of operations and improve legibility by identifying scalar and vector quantities.

Consider the scalar field, (F), and the vector fields ü(r) and ü(F). Using index notation, prove the following identities: (a) V. (ø T) = ū . Vø + ¢ỹ ·õ. (b) V× (ø i) = pỹ ×ũ – ở × Vø. (c) V·(ũ x ū) = · ỹ × ũ – - Ÿ × ū. (d) V × (ũ x ĩ) = . ỹ ū – ūỹ · ū +ūỷ •ỡ – ủ · ỹ ū. Introduce parentheses on the right-hand side of these equations to indicate the order of operations and improve legibility by identifying scalar and vector quantities.

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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Equations and inequalities describe the relationship between two mathematical expressions.

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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

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I need the answer as soon as possible

Consider the scalar field, ø(r), and the vector fields ü(r) and ū(r). Using index
notation, prove the following identities:
(a) V. (ø T) = ū . Vo + ¢ỹ · õ.
(b) V× (ø t) = ¢ỹ ×ð – i x Vø.
(c) V·(ū× í) = · ỹ × ū – ū · ỹ x ū.
(d) V× (ũ x ī) = ở . ỹũ – ū ỹ ·ũ +ūÿ·¯ – ủ · ỹ ở.
V •
Introduce parentheses on the right-hand side of these equations to indicate the order
of operations and improve legibility by identifying scalar and vector quantities.

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