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Saturday, 31 October

JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 18 March 2021, Shift 2, Maths Q80

Question 80 of 90 in this shift, Maths question 20 of 30, Section A.

Let a⃗\vec{a} and b⃗\vec{b} be two non-zero vectors perpendicular to each other and ∣a⃗∣=∣b⃗∣\left|\vec{a}\right|=\left|\vec{b}\right|. If ∣a⃗×b⃗∣=∣a⃗∣\left|\vec{a}\times\vec{b}\right|=\left|\vec{a}\right|, then the angle between the vectors (a⃗+b⃗+(a⃗×b⃗))\left(\vec{a}+\vec{b}+(\vec{a}\times\vec{b})\right) and a⃗\vec{a} is equal to :
  1. (1)cos⁡−1(13)\cos^{-1}\left(\frac{1}{\sqrt{3}}\right)Official answer
  2. (2)cos⁡−1(12)\cos^{-1}\left(\frac{1}{\sqrt{2}}\right)
  3. (3)sin⁡−1(13)\sin^{-1}\left(\frac{1}{\sqrt{3}}\right)
  4. (4)sin⁡−1(16)\sin^{-1}\left(\frac{1}{\sqrt{6}}\right)

Official answer

Option 1

NTA final key.

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

Same idea in other shifts

Asked 13× 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. 5 Apr 2024, Shift 2 · Q19Consider three vectors a⃗,b⃗,c⃗\vec{a}, \vec{b}, \vec{c}. Let ∣a⃗∣=2|\vec{a}| = 2, ∣b⃗∣=3|\vec{b}| = 3 and a⃗=b⃗×c⃗\vec{a} = \vec{b} \times \vec{c}. If…HardSingle correct
  3. 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
  4. 30 Jan 2024, Shift 1 · Q18Let a⃗=a1i^+a2j^+a3k^\vec{a}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k} and b⃗=b1i^+b2j^+b3k^\vec{b}=b_1\hat{i}+b_2\hat{j}+b_3\hat{k} be two vectors such that ∣a⃗∣=1|\vec{a}|=1,…HardSingle correct
  5. 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
  6. 11 Apr 2023, Shift 2 · Q29Let a⃗=i^+2j^+3k^\vec{a} = \hat{i} + 2\hat{j} + 3\hat{k} and b⃗=i^+j^−k^\vec{b} = \hat{i} + \hat{j} - \hat{k}. If c⃗\vec{c} is a vector such that…HardNumerical value
  7. 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
  8. 26 Jul 2022, Shift 1 · Q15Let a→=αi^+j^−k^\overrightarrow{\mathrm{a}} = \alpha \hat{i} + \hat{j} - \hat{k} and…MediumSingle 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 108 of the 174 JEE Main shifts held from 2017 to 2026.