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Saturday, 31 October

JEE Main 2021 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 3 August 2021, Shift 1, Maths Q68

Question 68 of 90 in this shift, Maths question 8 of 30, Section A.

A plane passes through the points A(1, 2, 3), B(3, 5, 2) and C(2, 1, 5). If P(aa, bb, cc) be a point such that a(b+c)=bca(b + c) = bc, then the acute angle which the line OP (O is the origin and P≠OP \neq O) makes with the plane is
  1. (1)π4\frac{\pi}{4}
  2. (2)sin⁡−1(13)\sin^{-1}\left(\frac{1}{\sqrt{3}}\right)Official answer
  3. (3)cos⁡−1(13)\cos^{-1}\left(\frac{1}{\sqrt{3}}\right)
  4. (4)π6\frac{\pi}{6}

Official answer

Option 2

NTA final key.

Chapter
Three Dimensional Geometry
Topic
Planes in 3D
Idea tested
Plane Through Three Points

Same idea in other shifts

Asked 3× in all
  1. 8 Apr 2023, Shift 2 · Q30Let P1P_1 be the plane 3x−y−7z=113x - y - 7z = 11 and P2P_2 be the plane passing through the points (2,−1,0)(2, -1, 0), (2,0,−1)(2, 0, -1), and (5,1,1)(5, 1, 1).…HardNumerical value
  2. 4 Aug 2021, Shift 1 · Q88If the distance between the point (a,−1,1)(a, -1, 1) (a>0)(a>0) and the plane passing through the points (1,−2,1)(1, -2, 1), (3,1,0)(3, 1, 0) and (2,0,1)(2, 0, 1)…MediumNumerical 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.