Further Mathematics-Vector

~HeBe~_@

我们一起分享与讨论吧！

Equation of plane

1)    Express the plane x - 3y = 0 as the set of all linear combinations of two nonparallel vectors.

2)    Find the equation of the plane that consist of all linear combinations of vector u = (1,-3,0) and vector  v =(1,2,6).

3)    Find the equation of the plane that is parallel to the plane x - 3y +7z = 2 and passing through (0,4,-1).

4)    Find the equation of the plane that passes through A(-1,2,1), B(0,1,1), C(7,-3,0).

5)    Find the equation of the plane that contains P(-1,2,5) and the line (x,y,z) = (3,-1,1) + t(-5,7,7).



[ 本帖最后由 ~HeBe~_@ 于 25-6-2006 01:18 AM 编辑 ]

~HeBe~_@

早安！
大家昨晚睡得温暖吗？

以上的问题没人会回答吗？



动动脑筋想想看吧！不会难的。

pisgon

还没学,连头绪都没有

dunwan2tellu

基本上 plane 的 equation 有三种写法

(i)r.n = a.n  (注意:那个 . 是 r dot n 的意思)

(ii) ax + by + cz + d = 0

(iii) r = a + sb + tc

第一种写法需要 normal vector to the plane , n , 和一个 point on the plane , a .

第二种写法是第一种的转换 i.e

r.(1,2,3) = 9 ===> x + 2y + 3z - 9 = 0

第三种写法需要3个 point on the plane , a,b,c . i.e if given three point A,B,C then plane equation , r = OA + s AB + t AC （这里 OA,AB,AC 都是 vector ; s,t 是 constant )

[ 本帖最后由 dunwan2tellu 于 25-6-2006 03:45 PM 编辑 ]

~HeBe~_@

难道没人对对这些问题感兴趣？

只有dunwan2tellu回答而已哦。。