Question

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=0

This 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 1

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.