Intersection of 3 Planes

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Transcription:

Intersection of 3 Planes With a partner draw diagrams to represent the six cases studied yesterday. Case 1: Three distinct parallel planes 1

Intersection of 3 Planes With a partner draw diagrams to represent the six cases studied yesterday. Case 1: Three distinct parallel planes 2

Intersection of 3 Planes With a partner draw diagrams to represent the six cases studied yesterday. Case 1: Three distinct parallel planes 3

Intersection of 3 Planes With a partner draw diagrams to represent the six cases studied yesterday. Case 1: Three distinct parallel planes 4

Intersection of 3 Planes With a partner draw diagrams to represent the six cases studied yesterday. Case 1: Three distinct parallel planes 5

Intersection of 3 Planes With a partner draw diagrams to represent the six cases studied yesterday. Case 1: Three distinct parallel planes 6

Intersection of 3 Planes With a partner draw diagrams to represent the six cases studied yesterday. Case 1: Three distinct parallel planes 7

Case 1: Three distinct parallel planes System is inconsistent System is consistent 8

Intersection of 3 Planes With a partner draw diagrams to represent the six cases studied yesterday. Case 1: Three distinct parallel planes 9

Case 1: Three distinct parallel planes Normals are Coplanar Normals are parallel Normals are not coplanar 10

Solution Normals are Coplanar Case 1: Three distinct parallel planes Normals are parallel Normals are not coplanar 11

Think: How can check to see if three normal vectors are coplanar? If they are not coplanar what do we then know? If they are coplanar, then what? How can we check to see if the normal vectors are parallel? 12

p_27_1_planealgebra.ppt 13

Determine if each system can be solved; then solve the system, or describe it. Group 1 Group 2 3x + y 2z = 12 x 5y + z = 8 12x + 4y 8z = 4 x +3y z = 10 2x + y +z = 8 x 2y + 2z = 4 Group 3 Group 4 4x 2y + 6z = 35 10x + 5y 15z = 20 6x 3y + 9z = 50 x 5y + 2z 10 = 0 x + 7y 2z + 6 = 0 8x + 5y + z 20 = 0 14

Group 1 3x + y 2z = 12 x 5y + z = 8 12x + 4y 8z = 4 15

Group 2 x +3y z = 10 2x + y +z = 8 x 2y + 2z = 4 16

Group 3 4x 2y + 6z = 35 10x + 5y 15z = 20 6x 3y + 9z = 50 17

Group 4 x 5y + 2z 10 = 0 x + 7y 2z + 6 = 0 8x + 5y + z 20 = 0 18

19

Attachments p_27_1_planealgebra.ppt