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In the product
\[
\begin{aligned}
\vec{F} & =q(\overrightarrow{\mathrm{v}} \times \overrightarrow{\mathrm{B}}) \\
& =q \overrightarrow{\mathrm{v}} \times\left(\mathrm{B} \overrightarrow{\mathrm{i}}+\mathrm{B} \overrightarrow{\mathrm{j}}+\mathrm{B}_{0} \overrightarrow{\mathrm{k}}\right)
\end{aligned}
\]
(2021)
\( \mathrm{P} \)
W)
For \( q=1 \) and \( \vec{v}=2 \hat{i}+4 \hat{j}+6 \hat{k} \) and
\[
\overrightarrow{\mathrm{F}}=4 \overrightarrow{\mathrm{i}}-20 \overrightarrow{\mathrm{j}}+12 \overrightarrow{\mathrm{k}}
\]
What will be the complete expression for \( \overrightarrow{\mathrm{B}} \) ?
(a) \( -6 \hat{\mathrm{i}}-6 \hat{\mathrm{j}}-8 \hat{\mathrm{k}} \)
(b) \( 8 \hat{\mathrm{i}}+8 \hat{\mathrm{j}}-6 \hat{\mathrm{k}} \)
(c) \( 6 \hat{\mathrm{i}}+6 \hat{\mathrm{j}}-8 \hat{\mathrm{k}} \)
(d) \( -8 \hat{\mathrm{i}}-8 \hat{\mathrm{j}}-6 \hat{\mathrm{k}} \)
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