JEE Main 2021 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 17 March 2021, Shift 1, Maths Q90

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

\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}

such that

\vec{a}\cdot\vec{b}=1

and

\vec{b}\cdot\vec{c}=-3

, then

\frac{1}{3}\left((\vec{a}\times\vec{b})\cdot\vec{c}\right)

is equal to __________.

Official answer

NTA final key.

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 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
4 Sep 2020, Shift 1 · Q67Let $x_0$ be the point of local maxima of $f(x) = \vec{a} \cdot (\vec{b} \times \vec{c})$ , where…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.