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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)