JEE Main 2023MathematicsVector AlgebraMediumMCQ

JEE Main 2023 — Vector Algebra Question with Solution

JEE Main 2023 (13 Apr Shift 2)

Question

Let |a→|=2,|b→|=3 and the angle between the vectors a→ and b→ be π4. Then |(a→+2b→)×(2a→-3b→)|2 is equal to

Choose an option

Show full solutionCorrect option: D
Correct answer
D882

Step-by-step explanation

Given,

|a→|=2,|b→|=3 and the angle between the vectors a→ and b→ be π4,

Now solving,

|(a→+2b→)×(2a→-3b→)|2

=|-3(a→×b→)+4(b→×a→)|2 as a→×a→=0 & b→×b→=0

=|7(b→×a→)|2 as b→×a→=-a→×b→

=49|a|2|b|2sin2π4

=49×4×9×12

=882

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Vector Algebra chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

About this question

This is a previous-year question from JEE Main 2023, covering the Vector Algebra chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.