Question

$The\ planes: 2x-y+4z=5 \ and \ 5x-2.5y+10z=6\ are$

• A. Perpendicular
• B. Parallel
• C. intersect y-axis
• D. passes through $(0,0,\frac 54)$

Answer 1

Answer: (B)

Parallel

Answer 2

The equations of the planes are
$2x - y + 4z = 5$ $.....(1)$

$5x - 2.5y + 10z = 6$ $.....(2)$

It can be seen that,
$\frac {a_1}{a_2} =\frac {2}{5}$

$\frac {b_1}{b_2}=\frac {-1}{-2.5}=\frac {2}{5 }$

$\frac {c_1}{c_2} =\frac {4}{10} = \frac {2}{5}$

$∴\frac {a_1}{a_2}=\frac {b_1}{b_2}=\frac {c_1}{c_2}$

Therefore, the given planes are parallel.

Hence, the correct answer is B.