Question

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______.

Answer 1

The Answer is 11