Begin2.DVI

Appendix D

Solutions to Selected Problems

Chapter 6

I6-1. (a)A~+B~= 9ˆe 1 +eˆ 2 + 3ˆe 3 (b) 6A~− 3 B~= 15ˆe 2 (c)A~+ 2B~= 15ˆe 1 + 5ˆe 3

I6-2.
A~+B~=C~
A~+D~ =B~

Since the vectors are coplaner there exists scalar constantsα andβ such that

A~+αD~=βC~ This implies

A~+α(B~−A~) =β(A~+B~) or A~(1−α−β) +B~(α−β) =~ 0

SinceA~andB~ are linearly independent and noncolinear one can state that

1 =α+β and 0 =α−β

Solving these simultaneous equations givesα= 1/ 2 andβ= 1/ 2 which demonstrates

that the diagonals bisect one another.

I6-3.
LetA~+B~=C~and then by construction write

1

2

A~+D~+^1

2

B~=C~=A~+B~

so that

D~=^1

2

A~+^1

2

B~=^1

2

C~

Solutions Chapter 6