{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Ch_03 - Vector I - Exam_Soln

# Ch_03 - Vector I - Exam_Soln - Exam Problems of Vector...

This preview shows pages 1–5. Sign up to view the full content.

Exam Problems of Vector Differential Calculus

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Vector Differential Calculus Fundamentals Fundamentals 1. (05’) Prove (A) ( ) ( ) ( ) A B C B A C C A B (B) ( ) ( ) ( )( ) ( )( ) A B C D A C B D A D B C (C) ( ) ( ) ( ) ( ) ( ) ( ) A B C D A C D B B C D A A B D C A B C D Solution: (A) ( ) ( ) ( ) A B C B A C C A B ( ) ( ) [( ) ( ) ] ( ) ( ) A B C B C A B A C C A B B A C C A B (B) ( ) ( ) ( )( ) ( )( ) A B C D A C B D A D B C Let ( ) X A B , then ( ) ( ) X C D X C D ( ) ( ) {( ) } { ( ) ( )} ( )( ) ( )( ) A B C D A B C D B A C A B C D A C B D A D B C (C) ( ) ( ) ( ) ( ) ( ) ( ) A B C D A C D B B C D A A B D C A B C D By middle factor rule, ( ) ( ) ( ( )) ( ( )) A B C D A C D B B C D A A C D B B C D A or ( ) ( ) (( ) ) (( ) ) A B C D A B D C A B C D A B D C A B C D
Vector Differential Calculus Fundamentals (Continued) (or for (A) ( ) ( ) ( ) A B C B A C C A B Set 1 2 3 a a a A i j k , 1 2 3 b b b B i j k , 1 2 3 c c c C i j k 1 2 3 1 2 3 1 2 3 2 3 1 3 1 2 1 2 3 2 3 1 3 1 2 1 2 3 2 3 3 2 1 3 3 1 1 2 2 1 LHS a a a b b b c c c b b b b b b a a a c c c c c c a a a b c b c b c b c b c b c i j k i j k i j k i j k i j k 2 1 2 2 2 1 3 1 3 3 3 1 1 1 2 1 2 1 3 2 3 3 3 2 1 1 3 1 3 1 2 2 3 2 3 2 LHS a b c a b c a b c a b c a b c a b c a b c a b c a b c a b c a b c a b c i j k 1 1 2 2 3 3 a c a c a c A C