JEE Mains · Maths · STD 12 - 11. three dimension geometry
Let the line \(\ell: x =\frac{1- y }{-2}=\frac{ z -3}{\lambda}, \lambda \in R\) meet the plane \(P : x +2 y +3 z =4\) at the point \((\alpha, \beta, \gamma)\). If the angle between the line \(\ell\) and the plane \(P\) is \(\cos ^{-1}\left(\sqrt{\frac{5}{14}}\right)\), then \(\alpha+2 \beta+6 \gamma\) is equal to
- A \(11\)
- B \(10\)
- C \(12\)
- D \(13\)
Answer & Solution
Correct Answer
(A) \(11\)
Step-by-step Solution
Detailed explanation
\(\ell: x =\frac{ y -1}{2}=\frac{ z -3}{\lambda}, \lambda \in R\) DR's of line \(\ell(1,2, \lambda)\) DR's of normal vector of plane \(P: x+2 y+3 z=4\) are \((1,2,3)\) Now, angle between line \(\ell\) and plane \(P\) is given by…
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