JEE Mains · Maths · STD 12 - 11. three dimension geometry
Consider the three planes \(P_{1}: 3 x+15 y+21 z=9\) ; \(P _{2}: x -3 y - z =5,\) and ; \(P_{3}: 2 x+10 y+14 z=5\). Then, which one of the following is true ?
- A \(P _{1}\) and \(P _{2}\) are parallel
- B \(P _{1}\) and \(P _{3}\) are parallel
- C \(P _{2}\) and \(P _{3}\) are parallel
- D \(P _{1}, P _{2}\) and \(P _{3}\) all are parallel
Answer & Solution
Correct Answer
(B) \(P _{1}\) and \(P _{3}\) are parallel
Step-by-step Solution
Detailed explanation
\(P_{1}: x+5 y+7 z=3\) \(P_{2}: x-3 y-z=5\) \(P_{3}: x+5 y+7 z=\frac{5}{2}\) so \(P _{1}\) and \(P _{3}\) are parallel.
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