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Saturday, 31 October

JEE Main 2023 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 11 April 2023, Shift 1, Maths Q22

Question 22 of 90 in this shift, Maths question 22 of 30, Section B.

Let a line ll pass through the origin and be perpendicular to the lines l1:r⃗=(i^−11j^−7k^)+λ(i^+2j^+3k^), λ∈Rl_1 : \vec{r} = (\hat{i} - 11\hat{j} - 7\hat{k}) + \lambda(\hat{i} + 2\hat{j} + 3\hat{k}),\ \lambda \in \mathbb{R} and l2:r⃗=(−i^+k^)+μ(2i^+2j^+k^), μ∈Rl_2 : \vec{r} = (-\hat{i} + \hat{k}) + \mu(2\hat{i} + 2\hat{j} + \hat{k}),\ \mu \in \mathbb{R}. If P is the point of intersection of ll and l1l_1, and Q(α,β,γ)Q(\alpha, \beta, \gamma) is the foot of perpendicular from P on l2l_2, then 9(α+β+γ)9(\alpha + \beta + \gamma) is equal to ____________.

Official answer

5

NTA final key.

Chapter
Three Dimensional Geometry
Topic
Lines in 3D
Idea tested
Line Perpendicular to Two Given Lines

Same idea in other shifts

Asked 7× in all
  1. 2 Apr 2026, Shift 1 · Q15Let a line L passing through the point (1,1,1)(1, 1, 1) be perpendicular to both the vectors 2i^+2j^+k^2\hat i+2\hat j+\hat k and…MediumSingle correct
  2. 8 Apr 2026, Shift 2 · Q23Let a line L1L_1 pass through the origin and be perpendicular to the lines…MediumNumerical value
  3. 7 Apr 2025, Shift 2 · Q16If the equation of the line passing through the point (0,−12,0)\left(0,-\frac{1}{2},0\right) and perpendicular to the lines…MediumSingle correct
  4. 30 Jan 2024, Shift 2 · Q17Let L1:r⃗=(i^−j^+2k^)+λ(i^−j^+2k^),λ∈RL_1: \vec{r} = (\hat{i} - \hat{j} + 2\hat{k}) + \lambda(\hat{i} - \hat{j} + 2\hat{k}), \lambda \in \mathbb{R},…MediumSingle correct
  5. 31 Jan 2024, Shift 1 · Q15The distance of the point Q(0,2,−2)Q(0,2,-2) form the line passing through the point P(5,−4,3)P(5,-4,3) and perpendicular to the lines…MediumSingle correct
  6. 25 Feb 2021, Shift 2 · Q88A line ‘ll’ passing through origin is perpendicular to the lines l1:r⃗=(3+t)i^+(−1+2t)j^+(4+2t)k^l_1: \vec{r} = (3+t)\hat{i} + (-1+2t)\hat{j} + (4+2t)\hat{k}…HardNumerical value

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.