Let $|\vec{a}|=2$, $|\vec{b}|=3$ and the angle between the vectors $\vec{a}$ and $\vec{b}$ be $\frac{\pi}{4}$. Then $\left|(\vec{a}+2\vec{b})\times(2\vec{a}-3\vec{b})\right|^2$ is equal to

JEE Main 2023 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 13 April 2023, Shift 2, Maths Q17

Question 17 of 90 in this shift, Maths question 17 of 30, Section A.

Let

|\vec{a}|=2

|\vec{b}|=3

and the angle between the vectors

\vec{a}

and

\vec{b}

\frac{\pi}{4}

. Then

\left|(\vec{a}+2\vec{b})\times(2\vec{a}-3\vec{b})\right|^2

is equal to

(1) $441$
(2) $882$ Official answer
(3) $482$
(4) $841$

Official answer

Option 2

NTA final key.

Chapter: Vector Algebra
Topic: Cross Product
Idea tested: Anti-commutativity and Distributivity

Same topic in other shifts

All Cross Product questions

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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.