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[M2] 求巴打carry 呢題數>.< 諗緊都諗唔到

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求巴打carry 呢題數>.< 諗緊都諗唔到

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

主要想問好(D) 知道要用l PQ.n l/lnl   但正係知一點係(0,0,0)  仲有一點唔知, 另外想問(B) 係咪自己代入去
   

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2x+3y+4z=12
(2x+3y+4z)/sqrt(29)=12/sqrt29)
(2/sqrt(29) i + 3 /sqrt(29) j + 4/sqrt(29)k) dot (xi+yj+zk) = 12/sqrt(29)
distance from origin to the plane = magnitude of projection of (xi+yj+zj) onto the unit vector.
so the distance from origin to the plane is 12/sqrt(29)

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(b) find any two points that satisfy 2x+3y+4z=12.
for example (6,0,0) or (0, 4, 0) or (0,0, 3)

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sorry, kindly explain how to get those point from (b) and  I just found out I don't understand C as well. Please help. Thank you em46 em46 em46

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just pick any point (x,y,z) that satisfy 2x+3y+4z=12 will do for part (b)
put y=z=0 you will have x=6  we have the point (6, 0, 0)
put x=z=0 you will have y=4  we have the point (0, 4, 0)
put x=y=0 you will have z=3  we have the point (0, 0, 3)
or you can put x=3, y=2, z=0 then we have the point (3,2,0)

for part (c) just simply find the difference of two position vectors found in (b)
if you take (6, 0, 0) and (0, 4,0) then the vector will be 6i-4j or 3i-2j
if you take (3, 2, 0) and (0, 0,3) then the vector will be 3i+2j-3k

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