Let $\vec{a}$, $\vec{b}$ and $\vec{c}$ be three vectors such that $|\vec{a}|=\sqrt3$, $|\vec{b}|=5$, $\vec{b}\cdot\vec{c}=10$ and the angle between $\vec{b}$ and $\vec{c}$ is $\frac{\pi}{3}$. If $\vec{a}$ is perpendicular to the vector $\vec{b}\times\vec{c}$, then $|\vec{a}\times(\vec{b}\times\vec{c})|$ is equal to ______.

JEE Main 2020 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 9 January 2020, Shift 2, Maths Q75

Question 75 of 75 in this shift, Maths question 25 of 25, Section B.

Let

\vec{a}

\vec{b}

and

\vec{c}

be three vectors such that

|\vec{a}|=\sqrt3

|\vec{b}|=5

\vec{b}\cdot\vec{c}=10

and the angle between

\vec{b}

and

\vec{c}

\frac{\pi}{3}

. If

\vec{a}

is perpendicular to the vector

\vec{b}\times\vec{c}

, then

|\vec{a}\times(\vec{b}\times\vec{c})|

is equal to ______.

Official answer

30.00

NTA final key (Jan 2020).

Chapter: Vector Algebra
Topic: Cross Product
Idea tested: Magnitude and Sine Formula

Same idea in other shifts

Asked 6× in all

4 Apr 2026, Shift 2 · Q15Let $\hat u$ and $\hat v$ be unit vectors inclined at an acute angle such that $|\hat u\times\hat v|=\frac{\sqrt3}{2}$ . If…HardSingle correct
6 Apr 2024, Shift 2 · Q19Let $\vec{a}=6\hat{i}+\hat{j}-\hat{k}$ and $\vec{b}=\hat{i}+\hat{j}$ . If $\vec{c}$ is a vector such that $|\vec{c}|\ge 6$ ,…HardSingle correct
11 Apr 2023, Shift 1 · Q11Let $\vec{a}$ be a non-zero vector parallel to the line of intersection of the two planes described by $\hat{i}+\hat{j},\ \hat{i}+\hat{k}$ …HardSingle correct
25 Jul 2022, Shift 1 · Q15Let $ABC$ be a triangle such that $\overrightarrow{BC}=\vec a$ , $\overrightarrow{CA}=\vec b$ , $\overrightarrow{AB}=\vec c$ ,…HardTwo statements
2 Apr 2017 (offline) · Q84Let $\vec{a}=2\hat{i}+\hat{j}-2\hat{k}$ and $\vec{b}=\hat{i}+\hat{j}$ . Let $\vec{c}$ be a vector such that $|\vec{c}-\vec{a}|=3$ ,…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 42 of the 174 JEE Main shifts held from 2017 to 2026.