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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceTwo statementsHardMulti-step

JEE Main 24 June 2022, Shift 2, Maths Q16

Question 16 of 90 in this shift, Maths question 16 of 30, Section A.

Let a^\hat{a} and b^\hat{b} be two unit vectors such that ∣(a^+b^)+2(a^×b^)∣=2|(\hat{a} + \hat{b}) + 2(\hat{a} \times \hat{b})| = 2. If θ∈(0,π)\theta \in (0, \pi) is the angle between a^\hat{a} and b^\hat{b}, then among the statements: (S1) : 2∣a^×b^∣=∣a^−b^∣2|\hat{a} \times \hat{b}| = |\hat{a} - \hat{b}| (S2) : The projection of a^\hat{a} on (a^+b^)(\hat{a} + \hat{b}) is 12\frac{1}{2}
  1. (1)Only (S1) is true.
  2. (2)Only (S2) is true.
  3. (3)Both (S1) and (S2) are true.Official answer
  4. (4)Both (S1) and (S2) are false.

Official answer

Option 3

NTA final key.

Chapter
Vector Algebra
Topic
Dot Product
Idea tested
Lagrange's Identity (Dot Product Form)

Same topic in other shifts

All Dot Product questions
  1. 2 Apr 2026, Shift 1 · Q14If a⃗\vec a and b⃗\vec b are two vectors such that ∣a⃗∣=2|\vec a|=2 and ∣b⃗∣=3|\vec b|=3, then the maximum value of…HardSingle correct
  2. 2 Apr 2026, Shift 2 · Q14Let the vectors a⃗=−i^+j^+3k^\vec{a} = -\hat{i} + \hat{j} + 3\hat{k} and b⃗=i^+3j^+k^\vec{b} = \hat{i} + 3\hat{j} + \hat{k}. For some…MediumSingle correct
  3. 2 Apr 2026, Shift 2 · Q16Two adjacent sides of a parallelogram PQRSPQRS are given by PQ⃗=j^+k^\vec{PQ} = \hat{j} + \hat{k} and PS⃗=i^−j^\vec{PS} = \hat{i} - \hat{j}. If the side…MediumSingle correct
  4. 2 Apr 2025, Shift 1 · Q11If a⃗\vec{a} is a nonzero vector such that its projections on the vectors 2i^−j^+2k^2\hat{i}-\hat{j}+2\hat{k}, i^+2j^−2k^\hat{i}+2\hat{j}-2\hat{k} and…MediumSingle correct
  5. 7 Apr 2025, Shift 2 · Q15Let a⃗\vec{a} and b⃗\vec{b} be the vectors of the same magnitude such that…MediumSingle correct
  6. 8 Apr 2025, Shift 2 · Q14Let a⃗=i^+2j^+k^\vec{a} = \hat{i} + 2\hat{j} + \hat{k} and b⃗=2i^+j^−k^\vec{b} = 2\hat{i} + \hat{j} - \hat{k}. Let c^\hat{c} be a unit vector in the plane of…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.