Q 11-03-088JEE MainJEE Main 2023 (24 Jan, Shift 1)Easy
Vectors $a\hat i+b\hat j+\hat k$ and $2\hat i-3\hat j+4\hat k$ are perpendicular to each other when $3a+2b=7$. The ratio of $a$ to $b$ is $\dfrac x2$. The value of $x$ is ______.
Numerical value type. Enter your answer.
Answer: 1
Perpendicular: $2a-3b+4=0$. With $3a+2b=7$:
$4a-6b=-8$ and $9a+6b=21\Rightarrow13a=13\Rightarrow a=1$, $b=2$.
$\dfrac ab=\dfrac12=\dfrac x2\Rightarrow x=1$.
Solution by Sreeraj P, M.Sc Physics