JEE Main 2023 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 15 April 2023, Shift 1, Maths Q16

Question 16 of 90 in this shift, Maths question 16 of 30, Section A.

Let

S

be the set of all

(\lambda,\mu)

for which the vectors

\lambda\hat{i}-\hat{j}+\hat{k}

\hat{i}+2\hat{j}+\mu\hat{k}

and

3\hat{i}-4\hat{j}+5\hat{k}

, where

\lambda-\mu=5

, are coplanar, then

\sum_{(\lambda,\mu)\in S}80\left(\lambda^2+\mu^2\right)

is equal to

(1) $2130$
(2) $2210$
(3) $2290$ Official answer
(4) $2370$

Official answer

Option 3

NTA final key.

Chapter: Vector Algebra
Topic: Triple Products
Idea tested: Solving for Unknown in Coplanarity

Same idea in other shifts

Asked 7× in all

12 Apr 2023, Shift 1 · Q16Let $a, b, c$ be three distinct real numbers, none equal to one. If the vectors $a\hat{i}+\hat{j}+\hat{k}$ , $\hat{i}+b\hat{j}+\hat{k}$ and…MediumSingle correct
28 Jun 2022, Shift 1 · Q24If $\vec{a}=2\hat{i}+\hat{j}+3\hat{k}$ , $\vec{b}=3\hat{i}+3\hat{j}+\hat{k}$ and $\vec{c}=c_1\hat{i}+c_2\hat{j}+c_3\hat{k}$ are coplanar…MediumNumerical value
30 Jun 2022, Shift 1 · Q17Let a vector $\vec{c}$ be coplanar with the vectors $\vec{a} = -\hat{i} + \hat{j} + \hat{k}$ and $\vec{b} = 2\hat{i} + \hat{j} - \hat{k}$ .…HardSingle correct
25 Jul 2021, Shift 1 · Q71Let the vectors $(2+a+b)\hat{i}+(a+2b+c)\hat{j}-(b+c)\hat{k}$ , $(1+b)\hat{i}+2b\hat{j}-b\hat{k}$ and…MediumSingle correct
25 Jul 2021, Shift 2 · Q80Let a, b and c be distinct positive numbers. If the vectors $a\hat{i}+a\hat{j}+c\hat{k}$ , $\hat{i}+\hat{k}$ and…MediumSingle correct
9 Jan 2020, Shift 1 · Q73If the vectors, $\vec{p}=(a+1)\hat{i}+a\hat{j}+a\hat{k}$ , $\vec{q}=a\hat{i}+(a+1)\hat{j}+a\hat{k}$ and…MediumNumerical value

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.