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Friday, 9 October

JEE Main 2024 · MathsMultiple choiceTwo statementsHardMulti-step

JEE Main 9 April 2024, Shift 2, Maths Q17

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

Between the following two statements: Statement I : Let a⃗=i^+2j^−3k^\vec{a}=\hat{i}+2\hat{j}-3\hat{k} and b⃗=2i^+j^−k^\vec{b}=2\hat{i}+\hat{j}-\hat{k}. Then the vector r⃗\vec{r} satisfying a⃗×r⃗=a⃗×b⃗\vec{a}\times\vec{r}=\vec{a}\times\vec{b} and a⃗⋅r⃗=0\vec{a}\cdot\vec{r}=0 is of magnitude 10\sqrt{10}. Statement II : In a triangle ABCABC, cos⁡2A+cos⁡2B+cos⁡2C≥−32\cos 2A+\cos 2B+\cos 2C\ge-\frac{3}{2}.
  1. (1)Both Statement I and Statement II are correct.
  2. (2)Both Statement I and Statement II are incorrect.
  3. (3)Statement I is correct but Statement II is incorrect.
  4. (4)Statement I is incorrect but Statement II is correct.Official answer

Official answer

Option 4

NTA final key.

Chapter
Vector Algebra
Topic
Cross Product
Idea tested
Solving Vector Equations with Cross Products

Same idea in other shifts

Asked 8× in all
  1. 5 Apr 2026, Shift 1 · Q14Let a⃗=7i^+j^−k^\vec{a} = \sqrt{7}\hat{i} + \hat{j} - \hat{k} and b⃗=j^+2k^\vec{b} = \hat{j} + 2\hat{k}. If r⃗\vec{r} is a vector such that…MediumSingle correct
  2. 6 Apr 2026, Shift 1 · Q23If a⃗=i^+j^+k^\vec{a}=\hat{i}+\hat{j}+\hat{k}, b⃗=j^−k^\vec{b}=\hat{j}-\hat{k} and c⃗\vec{c} be three vectors such that a⃗×c⃗=b⃗\vec{a}\times\vec{c}=\vec{b}…MediumNumerical value
  3. 8 Apr 2026, Shift 2 · Q14Let a⃗=4i^−j^+3k^\vec{a} = 4\hat{i} - \hat{j} + 3\hat{k}, b⃗=10i^+2j^−k^\vec{b} = 10\hat{i} + 2\hat{j} - \hat{k} and a vector c⃗\vec{c} be such that…MediumSingle correct
  4. 31 Jan 2024, Shift 1 · Q18Let a⃗=3i^+j^−2k^\vec{a}=3\hat{i}+\hat{j}-2\hat{k}, b⃗=4i^+j^+7k^\vec{b}=4\hat{i}+\hat{j}+7\hat{k} and c⃗=i^−3j^+4k^\vec{c}=\hat{i}-3\hat{j}+4\hat{k} be three vectors. If…MediumSingle correct
  5. 31 Jan 2024, Shift 2 · Q30Let a⃗=3i^+2j^+k^\vec{a}=3\hat{i}+2\hat{j}+\hat{k}, b⃗=2i^−j^+3k^\vec{b}=2\hat{i}-\hat{j}+3\hat{k} and c⃗\vec{c} be a vector such that…HardNumerical value
  6. 24 Jun 2022, Shift 1 · Q16Let a^,b^\hat{a}, \hat{b} be unit vectors. If c⃗\vec{c} be a vector such that the angle between a^\hat{a} and c⃗\vec{c} is π12\frac{\pi}{12},…HardSingle correct
  7. 16 Mar 2021, Shift 2 · Q63Let a⃗=i^+2j^−3k^\vec a=\hat i+2\hat j-3\hat k and b⃗=2i^−3j^+5k^\vec b=2\hat i-3\hat j+5\hat k. If r⃗×a⃗=b⃗×r⃗\vec r\times\vec a=\vec b\times\vec r,…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.