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Social ScienceHow can you tell when two planes A1 x + B1 y + C1 z = D1 and A2 x + B2 y + C2 z = D2 are parallel? Perpendicular? Give rea-sons for your answer.
How can you tell when two planes A1 x + B1 y + C1 z = D1 and A2 x + B2 y + C2 z = D2 are parallel? Perpendicular? Give rea-sons for your answer.
Expert Answer
Two planes are parallel if their normal vectors are parallel.
Normal vector of A1 x + B1 y + C1 z = D1 is (A1,B1,C1)
Normal vector of A2 x + B2 y + C2 z = D2 is (A2,B2,C2)
(A1,B1,C1) and (A2,B2,C2) will be parallel i...
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