Verified Solution • 2025–26 Session moderate

QJEEM23Pha527: JEE Main 2023 Physics - Class 11 JEEM23Pha527 Solution: Vectors and are perpendicular to each other when , the ratio of …

Vectors ai^+bj^+k^a\widehat i + b\widehat j + \widehat k and 2i^−3j^+4k^2\widehat i - 3\widehat j + 4\widehat k are perpendicular to each other when 3a+2b=73a + 2b = 7 , the ratio of aa to bb is x2{x \over 2} . The value of xx is ____________.

Step-by-Step Verified Solution

For two perpendicular vectors

amp;(ai^+bj^+k^)⋅(2i^−3j^+4k^)=0amp;2a−3b+4=0\begin{aligned}& (a \hat{i}+b \hat{j}+\hat{k}) \cdot(2 \hat{i}-3 \hat{j}+4 \hat{k})=0 \\\\& 2 a-3 b+4=0\end{aligned}

On solving, 2a−3b=−42 a-3 b=-4

Also given

3a+2b=73 a+2 b=7

We get a=1, b=2\mathrm{a}=1, \mathrm{~b}=2

amp;ab=x2⇒x=2ab=2×12amp;⇒x=1\begin{aligned}& \frac{\mathrm{a}}{\mathrm{b}}=\frac{\mathrm{x}}{2} \Rightarrow \mathrm{x}=\frac{2 \mathrm{a}}{\mathrm{b}}=\frac{2 \times 1}{2} \\\\& \Rightarrow \mathrm{x} =1\end{aligned}

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring