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Saturday, 31 October

JEE Main 2020 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 5 September 2020, Shift 1, Maths Q67

Question 67 of 75 in this shift, Maths question 17 of 25.

If the volume of a parallelopiped, whose coterminus edges are given by the vectors a⃗=i^+j^+nk^\vec{a}=\hat{i}+\hat{j}+n\hat{k}, b⃗=2i^+4j^−nk^\vec{b}=2\hat{i}+4\hat{j}-n\hat{k} and c⃗=i^+nj^+3k^\vec{c}=\hat{i}+n\hat{j}+3\hat{k} (n≥\ge0), is 158 cu.units, then :
  1. (1)n=7
  2. (2)n=9
  3. (3)b⃗⋅c⃗=10\vec{b}\cdot\vec{c}=10Official answer
  4. (4)a⃗⋅c⃗=17\vec{a}\cdot\vec{c}=17

Official answer

Option 3

NTA final key (Sep 2020).

Chapter
Vector Algebra
Topic
Triple Products
Idea tested
STP Geometric Interpretation

Same idea in other shifts

Asked 3× in all
  1. 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
  2. 8 Jan 2020, Shift 1 · Q66Let the volume of a parallelopiped whose coterminous edges are given by u⃗=i^+j^+λk^\vec{u}=\hat{i}+\hat{j}+\lambda\hat{k},…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.