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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 30 June 2022, Shift 1, Maths Q17

Question 17 of 90 in this shift, Maths question 17 of 30, Section A.

Let a vector c⃗\vec{c} be coplanar with the vectors a⃗=−i^+j^+k^\vec{a} = -\hat{i} + \hat{j} + \hat{k} and b⃗=2i^+j^−k^\vec{b} = 2\hat{i} + \hat{j} - \hat{k}. If the vector c⃗\vec{c} also satisfies the conditions c⃗⋅[(a⃗+b⃗)×(a⃗×b⃗)]=−42\vec{c} \cdot \left[\left(\vec{a}+\vec{b}\right) \times \left(\vec{a} \times \vec{b}\right)\right] = -42 and (c⃗×(a⃗−b⃗))⋅k^=3\left(\vec{c} \times \left(\vec{a} - \vec{b}\right)\right) \cdot \hat{k} = 3, then the value of ∣c⃗∣2\left|\vec{c}\right|^2 is equal to :
  1. (1)2424
  2. (2)2929
  3. (3)3535Official answer
  4. (4)4242

Official answer

Option 3

NTA final key.

Chapter
Vector Algebra
Topic
Triple Products
Idea tested
Solving for Unknown in Coplanarity

Same idea in other shifts

Asked 7× in all
  1. 12 Apr 2023, Shift 1 · Q16Let a,b,ca, b, c be three distinct real numbers, none equal to one. If the vectors ai^+j^+k^a\hat{i}+\hat{j}+\hat{k}, i^+bj^+k^\hat{i}+b\hat{j}+\hat{k} and…MediumSingle correct
  2. 15 Apr 2023, Shift 1 · Q16Let SS be the set of all (λ,μ)(\lambda,\mu) for which the vectors λi^−j^+k^\lambda\hat{i}-\hat{j}+\hat{k}, i^+2j^+μk^\hat{i}+2\hat{j}+\mu\hat{k} and…MediumSingle correct
  3. 28 Jun 2022, Shift 1 · Q24If a⃗=2i^+j^+3k^\vec{a}=2\hat{i}+\hat{j}+3\hat{k}, b⃗=3i^+3j^+k^\vec{b}=3\hat{i}+3\hat{j}+\hat{k} and c⃗=c1i^+c2j^+c3k^\vec{c}=c_1\hat{i}+c_2\hat{j}+c_3\hat{k} are coplanar…MediumNumerical value
  4. 25 Jul 2021, Shift 1 · Q71Let the vectors (2+a+b)i^+(a+2b+c)j^−(b+c)k^(2+a+b)\hat{i}+(a+2b+c)\hat{j}-(b+c)\hat{k}, (1+b)i^+2bj^−bk^(1+b)\hat{i}+2b\hat{j}-b\hat{k} and…MediumSingle correct
  5. 25 Jul 2021, Shift 2 · Q80Let a, b and c be distinct positive numbers. If the vectors ai^+aj^+ck^a\hat{i}+a\hat{j}+c\hat{k}, i^+k^\hat{i}+\hat{k} and…MediumSingle correct
  6. 9 Jan 2020, Shift 1 · Q73If the vectors, p⃗=(a+1)i^+aj^+ak^\vec{p}=(a+1)\hat{i}+a\hat{j}+a\hat{k}, q⃗=ai^+(a+1)j^+ak^\vec{q}=a\hat{i}+(a+1)\hat{j}+a\hat{k} 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.