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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 27 July 2022, Shift 2, Maths Q15

Question 15 of 90 in this shift, Maths question 15 of 30, Section A.

If the line of intersection of the planes ax+by=3ax + by = 3 and ax+by+cz=0ax + by + cz = 0, a > 0 makes an angle 30∘30^\circ with the plane y−z+2=0y - z + 2 = 0, then the direction cosines of the line are :
  1. (1)12,12,0\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 0Official answer
  2. (2)12,−12,0\frac{1}{\sqrt{2}}, -\frac{1}{\sqrt{2}}, 0Official answer
  3. (3)15,−25,0\frac{1}{\sqrt{5}}, -\frac{2}{\sqrt{5}}, 0
  4. (4)12,−32,0\frac{1}{2}, -\frac{\sqrt{3}}{2}, 0

Official answer

Options 1 and 2

NTA final key: multiple options accepted. Either option scored full marks.

Chapter
Three Dimensional Geometry
Topic
Planes in 3D
Idea tested
Direction of Line of Intersection

Same idea in other shifts

Asked 4× in all
  1. 26 Jul 2022, Shift 2 · Q15A vector a⃗\vec{a} is parallel to the line of intersection of the plane determined by the vectors i^, i^+j^\hat{i},\ \hat{i}+\hat{j} and the…MediumSingle correct
  2. 28 Jun 2022, Shift 1 · Q15If two distinct points Q, R lie on the line of intersection of the planes −x+2y−z=0-x+2y-z=0 and 3x−5y+2z=03x-5y+2z=0 and PQ=PR=18PQ=PR=\sqrt{18} where the…HardSingle correct
  3. 29 Jun 2022, Shift 1 · Q29Let P1:r⃗⋅(2i^+j^−3k^)=4P_1: \vec{r}\cdot(2\hat{i} + \hat{j} - 3\hat{k}) = 4 be a plane. Let P2P_2 be another plane which passes through the points…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.