JEE Main 2021MathematicsVector AlgebraEasyNumerical

JEE Main 2021 — Vector Algebra Question with Solution

JEE Main 2021 (20 Jul Shift 1)

Question

Let a→,b→,c→ be three mutually perpendicular vectors of the same magnitude and equally inclined at an angle θ, with the vector a→+b→+c→. Then 36cos22θ is equal to

Enter your answer

Show full solutionCorrect answer: 4
Correct answer
4

Step-by-step explanation

We have,

a→=b→=c→

a→·b→=b→·c→=c→·a→=0

Since, vectors are mutually perpendicular and of equally magnitude, hence let

a→=i^, b→=j^, c→=k^

Now,

a→+b→+c→·a→=i^+j^+k^·i^

⇒i^+j^+k^·i^=3·1·cosθ

⇒1+0+0=3·1·cosθ

⇒3cosθ=1

⇒cosθ=13

⇒cos2θ=2cos2θ-1=23-1

⇒cos2θ=-13

⇒cos22θ=19

⇒36cos22θ=4

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 2021, 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.