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Saturday, 31 October

JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 22 July 2021, Shift 2, Maths Q72

Question 72 of 90 in this shift, Maths question 12 of 30, Section A.

Let three vectors a⃗\vec{a}, b⃗\vec{b} and c⃗\vec{c} be such that a⃗×b⃗=c⃗\vec{a}\times\vec{b}=\vec{c}, b⃗×c⃗=a⃗\vec{b}\times\vec{c}=\vec{a} and ∣a⃗∣=2|\vec{a}|=2. Then which one of the following is not true ?
  1. (1)[a⃗ b⃗ c⃗]+[c⃗ a⃗ b⃗]=8[\vec{a}\ \vec{b}\ \vec{c}]+[\vec{c}\ \vec{a}\ \vec{b}]=8
  2. (2)a⃗×((b⃗+c⃗)×(b⃗−c⃗))=0⃗\vec{a}\times((\vec{b}+\vec{c})\times(\vec{b}-\vec{c}))=\vec{0}
  3. (3)∣3a⃗+b⃗−2c⃗∣2=51|3\vec{a}+\vec{b}-2\vec{c}|^2=51Official answer
  4. (4)Projection of a⃗\vec{a} on (b⃗×c⃗)(\vec{b}\times\vec{c}) is 22

Official answer

Option 3

NTA final key.

Chapter
Vector Algebra
Topic
Cross Product
Idea tested
Orthogonal Triad Expansion

Same topic in other shifts

All Cross Product questions
  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 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
  3. 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
  4. 6 Apr 2026, Shift 2 · Q15Let a⃗=2i^+3j^+3k^\vec{a}=2\hat{i}+3\hat{j}+3\hat{k} and b⃗=6i^+3j^+3k^\vec{b}=6\hat{i}+3\hat{j}+3\hat{k}. Then the square of the area of the triangle with…EasySingle correct
  5. 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
  6. 2 Apr 2025, Shift 1 · Q5Let ABCD be a tetrahedron such that the edges AB, AC and AD are mutually perpendicular. Let the areas of the triangles ABC, ACD and ADB be…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.