q12 a) Give examples of groups of three planes that satisfy each of the followin
ID: 2888466 • Letter: Q
Question
q12
a) Give examples of groups of three planes that satisfy each of the following conditions :
1- Three parallel planes
2- Two parallel planes and a third that meet them both
3- Three planes that meet in three lines
4- Three planes that meet in one line
5-Three planes that meet at a single point
For each group of planes ,fully explain why your planes meet each other in that way and Include a LanGraph of your planes
b) -Aplane has the scalar equation 3x-2y+5x+8=0 give the scalar equation of a plane that is:
1) Parallel to the original plane but has different values for A, B and c
2) Perpendicular to the original plane
Include LanGTraph of your planes
Explanation / Answer
a)
1. Three parallel Planes : x=0 , x=1, x=2
2. Two parallel planes : x=0 and x=1 and third that meet both y =2
3.Three planes that meet in three lines : x=1, y=2, z=5
4- Three planes that meet in one line : x=0, y=0, x-y=0 , all meets on line z=0
5-Three planes that meet at a single point: x=0,y=0,z=0, all meets on origin (0,0,0)
b)
1) 3x-2y+5z +8 =0
Parallel plane to given plane is 3(x-a)-2(y-b)+z(z-c) =0 if plane passes throught (a,b,c)
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