7. Determine if each system of planes is consistent or inconsistent. If possible, solve the system. a) 3x+y-2z= 18 6x-4y+10z= -10 3x-5y+10z = 10 b) 2x+5y-3z = 12 3x-2y+3z=5 4x+10y-6z= -10 c) 2x-3y+2z = 10 5x-15y+5z=25 -4x+6y-4z=-4 d) 3x-5y-5z=1 -6x+10y+10z = -2 15x-25y-25z=20
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Question 3: Consider the three planes: π1 = 3x - y - 2z + 8 = 0 π2 = x - 5y + 4z - 2 = 0 π3 = x + 79y - 80z + 82 = 0 a) Using Normals, classify the intersection of the planes. b) Solve the system of equations by elimination and classify it as consistent or inconsistent. Marking Scheme (out of 11) - 2 marks for stating the Normals and analyzing whether they are parallel - 3 marks for calculating the triple scalar product and determining whether the planes are co-planar - 5 marks to solve for t, and then solve the system of equations by elimination, and stating the solution - 1 mark for stating whether the system of equations is consistent or inconsistent
Sri K.
Find the intersection of the planes: 9x - 4y + 6z = -74 and 6x + 4y + 3z = -28. A. x = -2 - 12t, y = 2 - 63t, z = -8 - 12t B. x = 12t, y = 63t, z = 12t C. x = -2 - 36t, y = 2 + 9t, z = -8 + 60t D. The planes are parallel.
Adi S.
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