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Let the line / : x = \(\frac{1-y}{2}=\frac{z-3}{\lambda}, \lambda \in R\) meet the plane P : x+2y +3z = 4 at the point \((\alpha, \beta, \lambda)\). If the angle between the line I and the plane P is \(cos^{-1}\bigg(\sqrt{\frac{5}{14}}\bigg)\) then \(\alpha+2\beta+6\lambda\) is equal to______.
Let the line / : x = \(\frac{1-y}{2}=\frac{z-3}{\lambda}, \lambda \in R\) meet the plane P : x+2y +3z = 4 at the point \((\alpha, \beta, \lambda)\). If the angle between the line I and the plane P is \(cos^{-1}\bigg(\sqrt{\frac{5}{14}}\bigg)\) then \(\alpha+2\beta+6\lambda\) is equal to______.
Updated On: Oct 17, 2024
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Correct Answer: 11
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The Answer is 11
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