MHT CET · Maths · Three Dimensional Geometry
If the angle between the planes \(x-2 y+3 z-5=0\) and \(x+\alpha y+2 z+7=0\) is \(\cos ^{-1}\left(\frac{1}{14}\right)\) then the difference between the values of \(\alpha\) is
- A \(\frac{12}{11}\)
- B \(\frac{62}{55}\)
- C \(\frac{31}{11}\)
- D \(\frac{8}{5}\)
Answer & Solution
Correct Answer
(B) \(\frac{62}{55}\)
Step-by-step Solution
Detailed explanation
\(\vec{n_1} = \langle 1, -2, 3 \rangle, \vec{n_2} = \langle 1, \alpha, 2 \rangle\) \(\cos \theta = \frac{|\vec{n_1} \cdot \vec{n_2}|}{||\vec{n_1}|| \cdot ||\vec{n_2}||}\)
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