Question

Using index notation, demonstrate mathematically the following equations: 1- u × v = -v × u 2- ? · (?a) = ?^2 a 3- ?^2 (ab) = a?^2 b + 2?a · ?b + b?^2 a 4- ? · (ab) = ?a · b + a? · b 5- ? × ?? = 0 6- ? · (? × V) = 0 7- ? · V ? V · ? (express each term in index notation and expand in Cartesian coordinates to prove the inequality) 8- (a × b) · (c × d) = (a · c)(b · d) - (a · d)(b · c)

          Using index notation, demonstrate mathematically the following equations:

1- u × v = -v × u

2- ? · (?a) = ?^2 a

3- ?^2 (ab) = a?^2 b + 2?a · ?b + b?^2 a

4- ? · (ab) = ?a · b + a? · b

5- ? × ?? = 0

6- ? · (? × V) = 0

7- ? · V ? V · ? (express each term in index notation and expand in Cartesian coordinates to prove the inequality)

8- (a × b) · (c × d) = (a · c)(b · d) - (a · d)(b · c)

Using index notation, demonstrate mathematically the following equations:

1- u × v = -v × u

2- ? · (?a) = ?^2 a

3- ?^2 (ab) = a?^2 b + 2?a · ?b + b?^2 a

4- ? · (ab) = ?a · b + a? · b

5- ? × ?? = 0

6- ? · (? × V) = 0

7- ? · V ? V · ? (express each term in index notation and expand in Cartesian coordinates to prove the inequality)

8- (a × b) · (c × d) = (a · c)(b · d) - (a · d)(b · c)

Added by Amanda M.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Using index notation, demonstrate mathematically the following equations: 1- u x v = -v x u 2- ∇ · (∇a) = ∇^2a 3- ∇^2(ab) = a∇^2b + 2∇a · ∇b + b∇^2a 4- ∇ · (ab) = ∇a · b + a∇ · b 5- ∇ × ∇ϕ = 0 6- ∇ · (∇ × V) = 0 7- ∇ · V ≠ V · ∇ (express each term in index notation and expand in Cartesian coordinates to prove the inequality) 8- (a × b) · (c × d) = (a · c)(b · d) - (a · d)(b · c)