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Saturday, 31 October

JEE Main 2021 · PhysicsMultiple choiceDiagram basedMediumCalculation

JEE Main 26 August 2021, Shift 1, Physics Q18

Question 18 of 90 in this shift, Physics question 18 of 30, Section A.

The magnitude of vectors OA→\overrightarrow{OA}, OB→\overrightarrow{OB} and OC→\overrightarrow{OC} in the given figure are equal. The direction of OA→+OB→−OC→\overrightarrow{OA}+\overrightarrow{OB}-\overrightarrow{OC} with xx-axis will be :

The figure, in words

x and y axes (dotted) meeting at O. Vector OA points up and to the right, 30° above the +x axis; vector OB points down and to the right, 60° below the +x axis (angle marked 60° between +x axis and OB); vector OC points up and to the left, 45° above the −x axis.
  1. (1)tan⁡−1(1−3−2)(1+3+2)\tan^{-1}\frac{(1-\sqrt{3}-\sqrt{2})}{(1+\sqrt{3}+\sqrt{2})}Official answer
  2. (2)tan⁡−1(3−1+2)(1+3−2)\tan^{-1}\frac{(\sqrt{3}-1+\sqrt{2})}{(1+\sqrt{3}-\sqrt{2})}
  3. (3)tan⁡−1(1+3−2)(1−3−2)\tan^{-1}\frac{(1+\sqrt{3}-\sqrt{2})}{(1-\sqrt{3}-\sqrt{2})}
  4. (4)tan⁡−1(3−1+2)(1−3+2)\tan^{-1}\frac{(\sqrt{3}-1+\sqrt{2})}{(1-\sqrt{3}+\sqrt{2})}

Official answer

Option 1

NTA final key.

Chapter
Motion in a Plane
Topic
Kinematics in 2D
Idea tested
Vector Component Resolution

Same idea in other shifts

Asked 6× in all
  1. 8 Apr 2024, Shift 1 · Q51Three vectors OP→\overrightarrow{OP}, OQ→\overrightarrow{OQ} and OR→\overrightarrow{OR} each of magnitude AA are acting as shown in figure.…EasyNumerical valueHas a figure
  2. 30 Jan 2024, Shift 2 · Q51A vector has magnitude same as that of A⃗=3i^+4j^\vec{A} = 3\hat{i} + 4\hat{j} and is parallel to B⃗=4i^+3j^\vec{B} = 4\hat{i} + 3\hat{j}. The xx and yy…EasyNumerical value
  3. 15 Apr 2023, Shift 1 · Q37A vector in x−yx-y plane makes an angle of 30° with y-axis. The magnitude of y-component of vector is 232\sqrt{3}. The magnitude of…EasySingle correct
  4. 27 Aug 2021, Shift 1 · Q4The resultant of these forces OP→\overrightarrow{OP}, OQ→\overrightarrow{OQ}, OR→\overrightarrow{OR}, OS→\overrightarrow{OS} and…MediumSingle correctHas a figure
  5. 4 Sep 2020, Shift 1 · Q3Starting from the origin at time t=0, with initial velocity 5j^5\hat{j} ms−1^{-1}, a particle moves in the x−yx-y plane with a constant…EasySingle 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. This question needs a figure we do not reproduce; it is described in words above. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.