In the product

$\overrightarrow{F}=q(\overrightarrow{v}\times \overrightarrow{B})$

$=q\overrightarrow{v}\times \left(B\hat{\mathrm{i}}+B\hat{\mathrm{j}}+B_0\hat{\mathrm{k}}\right)$

For $q=1$ and $\overrightarrow{v}=2\hat{\mathrm{i}}+4\hat{\mathrm{j}}+6\hat{\mathrm{k}}$ and $\overrightarrow{F}=4\hat{\mathrm{i}}-20\hat{\mathrm{j}}+12\hat{\mathrm{k}}$

What will be the complete expression for $\overrightarrow{B}$?

• A

  $-8\hat{\mathrm{ı}}-8\hat{\mathrm{j}}-6\hat{\mathrm{k}}$
• Correct answer
  B

  $-6\hat{\mathrm{ı}}-6\hat{\mathrm{j}}-8\hat{\mathrm{k}}$
• C

  $8\hat{\mathrm{i}}+8\hat{\mathrm{j}}-6\hat{\mathrm{k}}$
• D

  $6\hat{\mathrm{i}}+6\hat{\mathrm{j}}-8\hat{\mathrm{k}}$

Hence, the correct answer is option: 'B'.