a) Calculate: -8 + 8i(3)¹/2 b) Use the quadruple product to express the following expression (A x B) × (C x D) - C × [(A × B) × D] and (A x B). (C x D) - C-[(A × B) x D] c) Show that: div[ax (bx c)] = (a-c)div b (a - b)div c + b grad(a. c) - c grad)a - b) d) Show that: a rot b = brot a if b = (a.a)a= a² a
a) Calculate: -8 + 8i(3)¹/2 b) Use the quadruple product to express the following expression (A x B) × (C x D) - C × [(A × B) × D] and (A x B). (C x D) - C-[(A × B) x D] c) Show that: div[ax (bx c)] = (a-c)div b (a - b)div c + b grad(a. c) - c grad)a - b) d) Show that: a rot b = brot a if b = (a.a)a= a² a
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![a) Calculate:
+8i (3)¹/2
b) Use the quadruple product to express the following expressions:
(A x B) × (C x D) - C × [(A × B) × D]
and
(A x B). (C x D) - C· [(A × B) × D]
c) Show that:
-
div[ax (bx c)] = (a c)div b (a - b)div c + b grad(a.
c) - c grad)a. b)
d) Show that:
arot b = brot a
if b = (a.a)a= a² a](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7c543d67-0094-4dfa-858b-8f9b09e8b86c%2Fa238454a-bd27-454b-a222-34f93739a36a%2Fbtkl124_processed.png&w=3840&q=75)
Transcribed Image Text:a) Calculate:
+8i (3)¹/2
b) Use the quadruple product to express the following expressions:
(A x B) × (C x D) - C × [(A × B) × D]
and
(A x B). (C x D) - C· [(A × B) × D]
c) Show that:
-
div[ax (bx c)] = (a c)div b (a - b)div c + b grad(a.
c) - c grad)a. b)
d) Show that:
arot b = brot a
if b = (a.a)a= a² a
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