An electron moves through a uniform magnetic field $\vec{B}=B_0 \hat{i}+2 B_0 \hat{j} T$. At a particular instant of time, the velocity of electron is $\overrightarrow{\mathrm{u}}=3 \hat{i}+5 \hat{j} \mathrm{~m} / \mathrm{s}$. If the magnetic force acting on electron is $\overrightarrow{\mathrm{F}}=5 \mathrm{ekN}$, where $e$ is the charge of electron, then the value of $\mathrm{B}_0$ is ____$\mathrm{T}$.
JEE MAIN 2024, Diffcult
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$\vec{F}=q(\vec{v} \times \vec{B})$
$5 e \hat{k}=e(3 \hat{i}+5 \hat{j}) \times\left(B_0 \hat{i}+2 B_0 \hat{j}\right)$
$5 e \hat{k}=e\left(6 B_0 \hat{k}-5 B_0 \hat{k}\right)$
$\Rightarrow B_0=5 T$
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