Question
The planes: $2x - y + 4z = 5$ and $5x - 2.5y + 10z = 6$ are
(A) Perpendicular
(B) Parallel
(C) Intersect y-axis
(D) Pass through $\left( {0,0,\cfrac{5}{4}} \right)$
Three Dimensional Geometry — Class 12 Maths Solution
Step-by-step Solution
Option B is correct
The direction ratios of planes are $< 2, - 1,4 >$ and $< 5, - 2.5,10 >$
Here, $\cfrac{2}{5} = \cfrac{{ - 1}}{{ - 2.5}} = \cfrac{4}{{10}}$
which is true.
$\therefore$ The given planes are parallel.
NCERT & Exemplar solution for CBSE Class 12 Mathematics, Three Dimensional Geometry. Curated by Sachin Sharma. Free for all students.