JEE Main 2020 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 4 September 2020, Shift 1, Maths Q67

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

Let

x_0

be the point of local maxima of

f(x) = \vec{a} \cdot (\vec{b} \times \vec{c})

, where

\vec{a} = x\hat{i} - 2\hat{j} + 3\hat{k}

\vec{b} = -2\hat{i} + x\hat{j} - \hat{k}

and

\vec{c} = 7\hat{i} - 2\hat{j} + x\hat{k}

. Then the value of

\vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a}

x = x_0

is :

(1) $-30$
(2) $-22$ Official answer
(3) $-4$
(4) $14$

Official answer

Option 2

NTA final key (Sep 2020).

Chapter: Vector Algebra
Topic: Triple Products
Idea tested: STP Definition and Determinant

Same idea in other shifts

Asked 4× in all

16 Mar 2021, Shift 2 · Q84Let $\vec c$ be a vector perpendicular to the vectors $\vec a=\hat i+\hat j-\hat k$ and $\vec b=\hat i+2\hat j+\hat k$ . If…MediumNumerical value
17 Mar 2021, Shift 1 · Q90If $\vec{a}=\alpha\hat{i}+\beta\hat{j}+3\hat{k}$ , $\vec{b}=-\beta\hat{i}-\alpha\hat{j}-\hat{k}$ and $\vec{c}=\hat{i}-2\hat{j}-\hat{k}$ …MediumNumerical value
17 Mar 2021, Shift 2 · Q63Let O be the origin. Let $\overrightarrow{OP}=x\hat{i}+y\hat{j}-\hat{k}$ and $\overrightarrow{OQ}=-\hat{i}+2\hat{j}+3x\hat{k}$ ,…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.