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In the product
$\overrightarrow{\mathrm{F}} =\mathrm{q}(\vec{v} \times \overrightarrow{\mathrm{B}})$
$=\mathrm{q} \vec{v} \times\left(\mathrm{B} \hat{i}+\mathrm{B} \hat{j}+\mathrm{B}_{0} \hat{k}\right)$
For $\mathrm{q}=1$ and $\vec{v}=2 \hat{i}+4 \hat{j}+6 \hat{k}$ and
$\overrightarrow{\mathrm{F}}=4 \hat{i}-20 \hat{j}+12 \hat{k}$
What will be the complete expression for $\vec{B}$ ?
$-8 \hat{i}-8 \hat{j}-6 \hat{k}$
$-6 \hat{i}-6 \hat{j}-8 \hat{k}$
$8 \hat{i}+8 \hat{j}-6 \hat{k}$
$6 \hat{i}+6 \hat{j}-8 \hat{k}$
Solution
$\mathrm{F}=\mathrm{q}(\overrightarrow{\mathrm{V}} \times \overrightarrow{\mathrm{B}})$
By check options
$(C)$ $-6 \hat{i}-6 \hat{j}-8 \hat{k}$
$\left|\begin{array}{ccc}\mathrm{i} & \mathrm{j} & \mathrm{k} \\ 2 & 4 & 6 \\ -6 & -6 & -8\end{array}\right|$ $\overrightarrow{\mathrm{V}} \times \overrightarrow{\mathrm{B}}=\hat{\mathrm{i}}(-32+36)+\hat{\mathrm{j}}(-36+16)+\mathrm{K}(-12+24)$
$=4 \hat{i}-20 \hat{j}+12 \hat{k}$
