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

The Correct Option is B

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.