JEE Main 2020MathematicsVector AlgebraMediumMCQ

JEE Main 2020 — Vector Algebra Question with Solution

JEE Main 2020 (07 Jan Shift 1)

Question

A vector a→=αi^+2j^+βk^α,β∈R lies in the plane of the vectors, b→=i^+j^ and c→=i^-j^+4k^. If a→ bisects the angle between b→ and c→, then

Choose an option

Show full solutionCorrect option: C
Correct answer
Ca→⋅k^+2=0

Step-by-step explanation

As, a→ lies in the plane of the vectors b→ and c→, So, a→=λi^+j^2+i^+j^+4k^32=λ323i^+3j^+i^-j^+4k^=λ324i^+2j^+4k^
Compare with a→=ai^+2j^+βk^
2λ32=2⇒λ=32
a→=4i^+2j^+4k^
Not in option
So, now consider a→=μi^+j^2-i^-j^+4k^32
a→=μ323i^+3j^-i^+j^-4k^
=μ322i^+4j^-4k^
Compare with a→=αi^+2j^+βk^
4μ32=2⇒μ=322
a→=i^+2j^-2k^
a→.k^+2=0

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 2020, 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.