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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 27 July 2022, Shift 1, Maths Q12

Question 12 of 90 in this shift, Maths question 12 of 30, Section A. NTA dropped this question from the final key; it is left out of every count on this site.

Let a⃗=αi^+j^+βk^\vec{a} = \alpha\hat{i} + \hat{j} + \beta\hat{k} and b⃗=3i^−5j^+4k^\vec{b} = 3\hat{i} - 5\hat{j} + 4\hat{k} be two vectors, such that a⃗×b⃗=−i^+9i^+12k^\vec{a} \times \vec{b} = -\hat{i} + 9\hat{i} + 12\hat{k}. Then the projection of b⃗−2a⃗\vec{b} - 2\vec{a} on b⃗+a⃗\vec{b} + \vec{a} is equal to
  1. (1)2
  2. (2)395\dfrac{39}{5}
  3. (3)9
  4. (4)465\dfrac{46}{5}

Official answer

Dropped by NTA (marks given to all)

NTA final key.

Chapter
Vector Algebra
Topic
Cross Product
Idea tested
Determinant Calculation Method

Same idea in other shifts

Asked 2× in all
  1. 10 Apr 2023, Shift 1 · Q16Let O be the origin and the position vector of the point P be −i^−2j^+3k^-\hat{i}-2\hat{j}+3\hat{k}. If the position vectors of the points A, B and…MediumSingle correct
  2. 3 Aug 2021, Shift 2 · Q90Let a⃗=2i^+αj^+k^\vec{a} = 2\hat{i} + \alpha\hat{j} + \hat{k} and b⃗=βi^−5j^+γk^\vec{b} = \beta\hat{i} - 5\hat{j} + \gamma\hat{k}, where α\alpha, β\beta and…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.