assignment1_sol

# assignment1_sol - MATH1211/10-11(2/Asol1/TNK,SKC Department...

This preview shows pages 1–2. Sign up to view the full content.

MATH1211/10-11(2)/Asol1/TNK,SKC Department of Mathematics, The University of Hong Kong MATH1211 (2010–11, 2nd semester) Suggested solution to Assignment 1 Note : Some solutions given below are outline only. You may need to give more details in your solution. The parts that are typed in red color are remarks for you to read; they are not a part of the solution. 1. Note that k a × b k = k a kk b k sin(angle between a and b ) is two times the area of the triangle whose two of the sides are formed by a and b with the tails of a and b touching together to form a vertex. Hence the surface area of the tetrahedron is given by k a × b k + k c × a k + k b × c k + k ( b - a ) × ( c - a ) k 2 . 2. Let a = a 1 i + a 2 j + a 3 k , b = b 1 i + b 2 j + b 3 k and c = c 1 i + c 2 j + c 3 k . Then a × b = ( a 2 b 3 - a 3 b 2 ) i + ( a 3 b 1 - a 1 b 3 ) j + ( a 1 b 2 - a 2 b 1 ) k . Hence ( a × b ) × c = (( a 3 b 1 - a 1 b 3 ) c 3 - ( a 1 b 2 - a 2 b 1 ) c 2 ) i + (( a 1 b 2 - a 2 b 1 ) c 1 - ( a 2 b 3 - a 3 b 2 ) c 3 ) j +(( a 2 b 3 - a 3 b 2 ) c 2 - ( a 3 b 1 - a 1 b 3 ) c 1 ) k = (( a 2 c 2 + a 3 c 3 ) b 1 - ( b 2 c 2 + b 3 c 3 ) a 1 ) i + (( a 1 c 1 + a 3 c 3 ) b 2 - ( b 1 c 1 + b 3 c 3 ) a 2 ) j +(( a 1 c 1 + a 2 c 2 ) b 3 - ( b 1 c 1 + b 2 c 2 ) a 3 ) k = (( a 1 c 1 + a 2 c 2 + a 3 c 3 ) b 1 - ( b 1 c 1 + b 2 c 2 + b 3 c 3 ) a 1 ) i +(( a 1 c 1 + a 2 c 2 + a 3 c 3 ) b 2 - ( b 1 c 1 + b 2 c 2 + b 3 c 3 ) a 2 ) j +(( a 1 c 1 + a 2 c 2 + a 3 c 3 ) b 3 - ( b 1 c 1 + b 2 c 2 + b 3

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

assignment1_sol - MATH1211/10-11(2/Asol1/TNK,SKC Department...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online