# 查看完整版本 : 數學M2 求高手幫幫小弟諗左幾個鐘都諗唔到

HKGC 2017-3-1 05:45 AM

## 數學M2 求高手幫幫小弟諗左幾個鐘都諗唔到

consider the equation of the plane: 2x+3y+4z=12

(A) find a normal vector to the plane:  n vector=<2,3,4>
(B) find two different points in the plane.
(C) find a vector that parallels to the plane
(D)find the distance from the origin to the plane

ppresent 2017-3-1 05:50 PM

(B) yes, plug in any x and y and then find z
(C) any vector that is perpendicular to (2,3,4)
(D) To find the distance of the plane from the origin, you may think about it this way:
If I know the point where the vector (2,3,4) touches the plane, then I know that the vector to the point has its length equal to the distance of the plane from the origin.
so let it be some multiple c of (2,3,4). since c(2,3,4) is on the plane, we have
c [2(2) +3(3) + 4(4)]=12
c=12/29
i.e. The vector 12/29(2,3,4) touches the plane.
And the distance is the length of this vector = 12/sqrt(29).

[3] 2017-3-1 06:47 PM

[quote]原帖由 [i]HKGC[/i] 於 2017-3-1 05:45 AM 發表 [url=http://www.discuss.com.hk/redirect.php?goto=findpost&pid=457189303&ptid=26480295][img]http://www.discuss.com.hk/images/common/back.gif[/img][/url]
consider the equation of the plane: 2x+3y+4z=12

(A) find a normal vector to the plane:  n vector=
(B) find two different points in the plane.
(C) find a vector that parallels to the plane
(D)fin ... [/quote]
[img]http://sciencesoft.at/lpng/af59ed0029f4fe0441e6c899159065055257b0a.png&size=100[/img]

[3] 2017-3-2 12:18 PM

[img]http://sciencesoft.at/lpng/af59ed0029f4fe0441e6c899159065055257aeb.png&size=100[/img]

[[i] 本帖最後由 [3] 於 2017-3-2 12:38 PM 編輯 [/i]]