- UID
- 139395
- 热情
- 24
- 人气
- 0
- 主题
- 0
- 帖子
- 505
- 精华
- 0
- 积分
- 77
- 分享
- 0
- 记录
- 0
- 相册
- 0
- 好友
- 0
- 日志
- 0
- 在线时间
- 134 小时
- 注册时间
- 2008-3-11
- 阅读权限
- 20
- 最后登录
- 2010-3-13
升级 0% - UID
- 139395
- 热情
- 24
- 人气
- 0
- 主题
- 0
- 帖子
- 505
- 精华
- 0
- 积分
- 77
- 阅读权限
- 20
- 注册时间
- 2008-3-11
|
哎.....具体问题,,,,
9. [10 marks] Consider the parallelepiped given by the three vectors O􀀀!A, O􀀀􀀀!B and O􀀀!C in R3 as
shown.
/
K
ooooooo7
O A
C
B
D E
(a) Express the vector O􀀀􀀀!E as a linear combination of O􀀀!A, O􀀀􀀀!B and O􀀀!C.
(b) Let A = (2; 2; 5), B = (􀀀4; 3; 1) and C = (2;􀀀1; 1). Find O􀀀􀀀!E and jO􀀀􀀀!Ej.
(c) Let A = (􀀀2; 0; 0), B = (􀀀k; 3; 0) and C = (0; k; 1), for some k 2 R.
(i) For which values of k is the equation jO􀀀!Aj2 + jO􀀀􀀀!Bj2 + jO􀀀!Cj2 = jO􀀀􀀀!Ej2 satised?
(ii) Sketch the vectors O􀀀!A, O􀀀􀀀!B and O􀀀!C for the value(s) of k you just computed. What
are the angles between them?
(d) In general, when is the equation jO􀀀!Aj2 +jO􀀀􀀀!Bj2 +jO􀀀!Cj2 = |
|