Question

Choose the correct answer in Question
The planes 2x - y + 4z = 5 and 5x - 2.5y + 10z = 6 are
(a) perpendicular
(b) parallel
(c) intersect along Y-axis
(d) passes through $(0,0,\frac{5}{4})$

Answer 1

Here, dr's of both planes are (2, -1, 4) and (5, -2.5, 10). As $\frac{2}{5}=\frac{-1}{-2.5}=\frac{4}{10}\Rightarrow \frac{4}{10}=\frac{4}{10}=\frac{4}{10}$
Therefore, $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
Therefore, the given planes are parallel. So, the correct option is (b).