Which of the following sets of planes are parallel to each other?(a) 2x+3y+4z=8 and 3x+9y+12z=7(b) 2x+3y+4z=2 and 4x+6y+8z=9(c) 3x+2y+4z=0 and 3x+4y+2z=0(d) 2x+4y+8z=9 and 4x+2y+7z=0This question was addressed to me in an online quiz.Question is from Three Dimensional Geometry topic in section Three Dimensional Geometry of Mathematics – Class 12

Which of the following sets of planes are parallel to each other?(a) 2

1.	Which of the following sets of planes are parallel to each other?(a) 2x+3y+4z=8 and 3x+9y+12z=7(b) 2x+3y+4z=2 and 4x+6y+8z=9(c) 3x+2y+4z=0 and 3x+4y+2z=0(d) 2x+4y+8z=9 and 4x+2y+7z=0This question was addressed to me in an online quiz.Question is from Three Dimensional Geometry topic in section Three Dimensional Geometry of Mathematics – Class 12
Answer» Right option is (b) 2x+3y+4z=2 and 4x+6y+8z=9 Best EXPLANATION: If TWO planes are of the form \(A_1 x+B_1 y+C_1 z+D_1\)=0 and \(A_2 x+B_2 y+C_2 z+D_2\)=0, then they will be parallel if \(\FRAC{A_1}{A_2}=\frac{B_1}{B_2}=\frac{C_1}{C_2}\) Consider the planes 2x+3y+4z=2 and 4x+6y+8z=9 \(\frac{A_1}{A_2}=\frac{2}{4}\) \(\frac{B_1}{B_2}=\frac{3}{6}\) \(\frac{C_1}{C_2}=\frac{4}{8}\) \(\frac{2}{4}=\frac{3}{6}=\frac{4}{8}=\frac{1}{2}\) Hence, the above set of planes are parallel.

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