MHT CET · Maths · Three Dimensional Geometry
If the planes \(2 x-5 y+z=8\) and \(2 \lambda x-15 y+\lambda z+6=0\) are parallel to each other, then value of \(\lambda\) is
- A \(\frac{1}{3}\)
- B \(-3\)
- C 2
- D 3
Answer & Solution
Correct Answer
(D) 3
Step-by-step Solution
Detailed explanation
Given planes are parallel. Therefore normal vector to their plane is also parallel.
\(\therefore \frac{2}{2 \lambda}=\frac{-5}{-15}=\frac{1}{\lambda} \Rightarrow \frac{1}{\lambda}=\frac{1}{3} \Rightarrow \lambda=3\)
\(\therefore \frac{2}{2 \lambda}=\frac{-5}{-15}=\frac{1}{\lambda} \Rightarrow \frac{1}{\lambda}=\frac{1}{3} \Rightarrow \lambda=3\)
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