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Saturday, 31 October

JEE Main 2022 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 25 June 2022, Shift 1, Maths Q28

Question 28 of 90 in this shift, Maths question 28 of 30, Section B.

Let the lines L1\mathrm{L_1} : r⃗=λ(i^+2j^+3k^)\vec{r}=\lambda\left(\hat{i}+2\hat{j}+3\hat{k}\right), λ∈R\lambda\in\mathbf{R} L2\mathrm{L_2} : r⃗=(i^+3j^+k^)+μ(i^+j^+5k^)\vec{r}=\left(\hat{i}+3\hat{j}+\hat{k}\right)+\mu\left(\hat{i}+\hat{j}+5\hat{k}\right); μ∈R\mu\in\mathbf{R}, intersect at the point S. If a plane ax+by−z+d=0ax+by-z+d=0 passes through S and is parallel to both the lines L1\mathrm{L_1} and L2\mathrm{L_2}, then the value of a+b+da+b+d is equal to __________.

Official answer

5

NTA final key.

Chapter
Three Dimensional Geometry
Topic
Planes in 3D
Idea tested
Plane Through Point Parallel to Two Vectors

Same idea in other shifts

Asked 2× in all
  1. 28 Jul 2022, Shift 2 · Q76A plane P is parallel to two lines whose direction ratios are −2, 1, −3-2,\ 1,\ -3 and −1, 2, −2-1,\ 2,\ -2 and it contains the point (2, 2, −2)(2,\ 2,\ -2).…MediumSingle correct

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.