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Friday, 9 October

JEE Main 2023 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 11 April 2023, Shift 1, Maths Q11

Question 11 of 90 in this shift, Maths question 11 of 30, Section A.

Let 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} and i^−j^, j^−k^\hat{i}-\hat{j},\ \hat{j}-\hat{k}. If θ\theta is the angle between the vector a⃗\vec{a} and the vector b⃗=2i^−2j^+k^\vec{b} = 2\hat{i} - 2\hat{j} + \hat{k} and a⃗⋅b⃗=6\vec{a}\cdot\vec{b} = 6, then the ordered pair (θ,∣a⃗×b⃗∣)\left(\theta, |\vec{a}\times\vec{b}|\right) is equal to
  1. (1)(π4,36)\left(\frac{\pi}{4}, 3\sqrt{6}\right)
  2. (2)(π3,6)\left(\frac{\pi}{3}, 6\right)
  3. (3)(π3,36)\left(\frac{\pi}{3}, 3\sqrt{6}\right)
  4. (4)(π4,6)\left(\frac{\pi}{4}, 6\right)Official answer

Official answer

Option 4

NTA final key.

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. 25 Jul 2022, Shift 1 · Q15Let ABCABC be a triangle such that BC→=a⃗\overrightarrow{BC}=\vec a, CA→=b⃗\overrightarrow{CA}=\vec b, AB→=c⃗\overrightarrow{AB}=\vec c,…HardTwo statements
  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.