Let the line ℓ: 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 ℓ and the plane {\P} is \cos ^{-1} (\sqrt{\frac{5}{14}}), then \alpha+2 \beta+6 \gamma is equal to _______. [11-Apr-2023 shift 2]

JEE Mains 11-Apr-2023 Shift 2 Solved Paper

Section: Mathematics

Question : 25 of 90

Marks: +1, -0

Let the line ℓ:x=‌

1−y

−2

=‌

z−3

,λ∈R meet the plane P:x+2y+3z=4 at the point (α,β,γ). If the angle between the line ℓ and the plane P is cos−1(√‌

), then α+2β+6γ is equal to _______.

[11-Apr-2023 shift 2]

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