Let a line l pass through the origin and be perpendicular to the lines 1_1: { {\r}}^{\to}=\stackrel{\^}{ {\i}}-11 \stackrel{\^}{ {\j}}-7 \stackrel{\^}{ {\k}}+\lambda \stackrel{\^}{ {\i}}+2 \stackrel{\^}{ {\j}}+3 \stackrel{\^}{ {\k}}, \lambda \in \mathbb{R} and 1_2: { {\r}}^{\to}=-\stackrel{\^}{ {\i}}+\stackrel{\^}{ {\k}}+\mu 2 \stackrel{\^}{ {\i}}+2 \stackrel{\^}{ {\j}}+\stackrel{\^}{ {\k}}, \mu \in \mathbb{R}. If {\P} is the point of intersection of l and l_1, and {\Q}(\alpha, \beta, \gamma) is the foot of perpendicular from {\P} on l_2, then 9(\alpha+\beta+\gamma) is equal to ______. [11-Apr-2023 shift 1]

JEE Mains 11-Apr-2023 Shift 1 Solved Paper

Section: Mathematics

Question : 30 of 90

Marks: +1, -0

Let a line l pass through the origin and be perpendicular to the lines
11:

→

−11

−7

+λ

,λ∈ℝ and
12:

→

=−

+µ2

,µ∈ℝ.
If P is the point of intersection of l and l1, and Q(α,β,γ) is the foot of perpendicular from P on l2, then 9(α+β+γ) is equal to ______.

[11-Apr-2023 shift 1]

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