MHT CET · Maths · Three Dimensional Geometry
If the angle between the line \(x=\frac{\mathrm{y}-1}{2}=\frac{\mathrm{z}-3}{\lambda}\) and the plane \(x+2 y+3 z=4\) is \(\cos ^{-1} \sqrt{\frac{5}{14}}\), then the value of \(\lambda\) is
- A \(\frac{1}{3}\)
- B \(\frac{4}{5}\)
- C \(\frac{2}{3}\)
- D \(\frac{2}{5}\)
Answer & Solution
Correct Answer
(C) \(\frac{2}{3}\)
Step-by-step Solution
Detailed explanation
\(\vec{b} = \langle 1, 2, \lambda \rangle\), \(\vec{n} = \langle 1, 2, 3 \rangle\) \(\cos \theta = \sqrt{\frac{5}{14}} \implies \sin \theta = \sqrt{1 - \frac{5}{14}} = \frac{3}{\sqrt{14}}\)
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