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Friday, 9 October

JEE Main 2022 · MathsMultiple choiceTwo statementsHardMulti-step

JEE Main 25 July 2022, Shift 1, Maths Q15

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

Let ABCABC be a triangle such that BC→=a⃗\overrightarrow{BC}=\vec a, CA→=b⃗\overrightarrow{CA}=\vec b, AB→=c⃗\overrightarrow{AB}=\vec c, ∣a⃗∣=62|\vec a|=6\sqrt2, ∣b⃗∣=23|\vec b|=2\sqrt3 and b⃗⋅c⃗=12\vec b\cdot\vec c=12. Consider the statements : (S1) : ∣(a⃗×b⃗)+(c⃗×b⃗)∣−∣c⃗∣=6(22−1)\left|(\vec a\times\vec b)+(\vec c\times\vec b)\right|-|\vec c|=6(2\sqrt2-1) (S2) : ∠ACB=cos⁡−1(23)\angle ACB=\cos^{-1}\left(\sqrt{\frac{2}{3}}\right) Then
  1. (1)both (S1) and (S2) are true
  2. (2)only (S1) is true
  3. (3)only (S2) is trueOfficial answer
  4. (4)both (S1) and (S2) are false

Official answer

Option 3

NTA final key (2022 Session 2).

Chapter
Vector Algebra
Topic
Cross Product
Idea tested
Magnitude and Sine Formula

Same idea in other shifts

Asked 6× in all
  1. 4 Apr 2026, Shift 2 · Q15Let u^\hat u and v^\hat v be unit vectors inclined at an acute angle such that ∣u^×v^∣=32|\hat u\times\hat v|=\frac{\sqrt3}{2}. If…HardSingle correct
  2. 6 Apr 2024, Shift 2 · Q19Let a⃗=6i^+j^−k^\vec{a}=6\hat{i}+\hat{j}-\hat{k} and b⃗=i^+j^\vec{b}=\hat{i}+\hat{j}. If c⃗\vec{c} is a vector such that ∣c⃗∣≥6|\vec{c}|\ge 6,…HardSingle correct
  3. 11 Apr 2023, Shift 1 · Q11Let a⃗\vec{a} be a non-zero vector parallel to the line of intersection of the two planes described by i^+j^, i^+k^\hat{i}+\hat{j},\ \hat{i}+\hat{k}…HardSingle correct
  4. 9 Jan 2020, Shift 2 · Q75Let a⃗\vec{a}, b⃗\vec{b} and c⃗\vec{c} be three vectors such that ∣a⃗∣=3|\vec{a}|=\sqrt3, ∣b⃗∣=5|\vec{b}|=5, b⃗⋅c⃗=10\vec{b}\cdot\vec{c}=10 and the…MediumNumerical value
  5. 2 Apr 2017 (offline) · Q84Let a⃗=2i^+j^−2k^\vec{a}=2\hat{i}+\hat{j}-2\hat{k} and b⃗=i^+j^\vec{b}=\hat{i}+\hat{j}. Let c⃗\vec{c} be a vector such that ∣c⃗−a⃗∣=3|\vec{c}-\vec{a}|=3,…HardSingle 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 42 of the 174 JEE Main shifts held from 2017 to 2026.