Question

The planes: 2 x − y + 4 z = 5 and 5 x − 2.5 y + 10 z = 6 are (A) Perpendicular (B) Parallel (C) intersect y -axis (C) passes through

Answer 1

The equations of the planes are,

2x−y+4z=5(1)

5x−2.5y+10z=6(2)

Compare the equation of plane with general equation of planes ax+by+cz+d=0

Let a 1 , b 1 , c 1 and a 2 , b 2 , c 2 be the intercepts of the lines.

a 1 =2, b 1 =−1, c 1 =4 a 2 =5, b 2 =−2.5, c 2 =10

Calculate the respective ratios of each intercepts.

a 1 a 2 = 2 5 b 1 b 2 = −1 −2.5 = 2 5 c 1 c 2 = 2 5

It is observed that the respective ratios are equal.

a 1 a 2 = b 1 b 2 = c 1 c 2

Thus, the given planes are parallel.

The correct option is B.