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JEE Main 2023 — Mathematics in Physics Question with Solution

JEE Main 2023 (24 Jan Shift 1)

Question

Vectors ai^+bj^+k^ and 2i^-3j^+4k^ are perpendicular to each other when 3a+2b=7, the ratio of a to b is x2. The value of x is _____.

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Correct answer
1

Step-by-step explanation

Dot product of two perpendicular vectors will be zero. Therefore,

ai^+bj^+k^·2i^-3j^+4k^=0

⇒2a-3b+4=0   ...Eq(1)

As given in the question,

3a+2b=7   ...Eq(2)

From both equations, we get a=1 & b=2

Then, 

ab=x2⇒x=2ab=2×12

⇒  x=1

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About this question

This is a previous-year question from JEE Main 2023, covering the Mathematics in Physics chapter of Physics. 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.