\(The\ planes: 2x-y+4z=5 \ and \ 5x-2.5y+10z=6\ are\)
\(The\ planes: 2x-y+4z=5 \ and \ 5x-2.5y+10z=6\ are\)
- Perpendicular
- Parallel
- intersect y-axis
passes through \((0,0,\frac 54)\)
The Correct Option is B
Solution and Explanation
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.
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