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Problem 1.4 Using the following vectors A = a i+ 2y j+ 3z k B = 3y i – 2x j Check the product rules by calculating each term separately a) Divergence Product Rule (iv) V· (A x B) = B· (V × A) – A · (V × B) %3D

Problem 1.4 Using the following vectors A = a i+ 2y j+ 3z k B = 3y i – 2x j Check the product rules by calculating each term separately a) Divergence Product Rule (iv) V· (A x B) = B· (V × A) – A · (V × B) %3D

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Problem 1.4 Using the following vectors A = x î+ 2y j+ 3z k В 3 Зу і - 2х j Check the product rules by calculating each term separately a) Divergence Product Rule (iv) V. (Ах В) —DВ (VxА) — А (Vx В) || b) Gradient Product Rule (ii) V(A · B) = A × (V × B) + Вx (Vx А) + (A · V)B + (B· V)A c) Curl Product Rule (vi) V x (A x B) = (B · V)A – (A · V)B+A(V · B) – B(V· A)
Transcribed Image Text:Problem 1.4 Using the following vectors A = x î+ 2y j+ 3z k В 3 Зу і - 2х j Check the product rules by calculating each term separately a) Divergence Product Rule (iv) V. (Ах В) —DВ (VxА) — А (Vx В) || b) Gradient Product Rule (ii) V(A · B) = A × (V × B) + Вx (Vx А) + (A · V)B + (B· V)A c) Curl Product Rule (vi) V x (A x B) = (B · V)A – (A · V)B+A(V · B) – B(V· A)
Problem 1.5 Using the formal definition of the Laplacian, V²T + dy? Calculate Laplacian of the following functions Ta = x2 + 2xy + 3z + 4 a) b) Ti = sin x sin y sin z c) T. = -5x = e sin 4y cos 3z d) v = x² i+ 3xz2 j – 2xz k
Transcribed Image Text:Problem 1.5 Using the formal definition of the Laplacian, V²T + dy? Calculate Laplacian of the following functions Ta = x2 + 2xy + 3z + 4 a) b) Ti = sin x sin y sin z c) T. = -5x = e sin 4y cos 3z d) v = x² i+ 3xz2 j – 2xz k
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