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Saturday, 31 October

JEE Main 2021 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 22 July 2021, Shift 2, Maths Q80

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

Let a vector a⃗\vec{\mathrm{a}} be coplanar with vectors b⃗=2i^+j^+k^\vec{\mathrm{b}}=2\hat{i}+\hat{j}+\hat{k} and c⃗=i^−j^+k^\vec{\mathrm{c}}=\hat{i}-\hat{j}+\hat{k}. If a⃗\vec{\mathrm{a}} is perpendicular to d⃗=3i^+2j^+6k^\vec{\mathrm{d}}=3\hat{i}+2\hat{j}+6\hat{k}, and ∣a⃗∣=10|\vec{\mathrm{a}}|=\sqrt{10}. Then a possible value of [a⃗ b⃗ c⃗]+[a⃗ b⃗ d⃗]+[a⃗ c⃗ d⃗][\vec{\mathrm{a}}\ \vec{\mathrm{b}}\ \vec{\mathrm{c}}]+[\vec{\mathrm{a}}\ \vec{\mathrm{b}}\ \vec{\mathrm{d}}]+[\vec{\mathrm{a}}\ \vec{\mathrm{c}}\ \vec{\mathrm{d}}] is equal to :
  1. (1)−40-40
  2. (2)−42-42Official answer
  3. (3)−38-38
  4. (4)−29-29

Official answer

Option 2

NTA final key.

Same topic in other shifts

All Triple Products questions
  1. 6 Apr 2024, Shift 2 · Q18Let a⃗=2i^+j^−k^\vec{a}=2\hat{i}+\hat{j}-\hat{k}, b⃗=((a⃗×(i^+j^))×i^)×i^\vec{b}=\left(\left(\vec{a}\times(\hat{i}+\hat{j})\right)\times\hat{i}\right)\times\hat{i}. Then…MediumSingle correct
  2. 1 Feb 2024, Shift 1 · Q19Let a⃗=−5i^+j^−3k^\vec{a}=-5\hat{i}+\hat{j}-3\hat{k}, b⃗=i^+2j^−4k^\vec{b}=\hat{i}+2\hat{j}-4\hat{k} and…MediumSingle correct
  3. 6 Apr 2023, Shift 1 · Q15Let the position vectors of the points A, B, C and D be 5i^+5j^+2λk^5\hat i+5\hat j+2\lambda\hat k, i^+2j^+3k^\hat i+2\hat j+3\hat k,…MediumSingle correct
  4. 6 Apr 2023, Shift 2 · Q17The sum of all values of α\alpha, for which the points whose position vectors are i^−2j^+3k^\hat{i}-2\hat{j}+3\hat{k},…MediumSingle correct
  5. 6 Apr 2023, Shift 2 · Q18Let the vectors a⃗,b⃗,c⃗\vec{a},\vec{b},\vec{c} represent three coterminous edges of a parallelopiped of volume V. Then the volume of the…MediumSingle correct
  6. 8 Apr 2023, Shift 2 · Q16Let the vectors u⃗1=i^+j^+ak^\vec{u}_1 = \hat{i} + \hat{j} + a\hat{k}, u⃗2=i^+bj^+k^\vec{u}_2 = \hat{i} + b\hat{j} + \hat{k} and…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 108 of the 174 JEE Main shifts held from 2017 to 2026.