In the product → F = q ( → v × → B ) = q → v × (B ^ i + B ^ j + B _...

4\overset{^}{ı} - 20\overset{^}{ȷ} + 12k = ( 2\overset{^}{ı} + 4\overset{^}{ȷ} + 6\overset{^}{k} ) \times \left(B\overset{^}{ı} + B\overset{^}{ȷ} + {B}_{o}\overset{^}{k}\right)

4\overset{^}{ı} - 20\overset{^}{ȷ} + 12\overset{^}{k} = \left|\begin{cases}+ \overset{^}{ı} & - \overset{^}{ȷ} & + \overset{^}{k} \\ 2 & 4 & 6 \\ B & B & {B}_{0}\end{cases}\right|

= \left(4{B}_{0} - 6B\right)\overset{^}{ı} - \left(2{B}_{0} - 6B\right)\overset{^}{ȷ} + ( 2B - 4B ) \overset{^}{k}

$4{B}_{0} - 6B = 4$

$2{B}_{0} - 6B = 20$

$2B - 4B = 12 ⇒ B = 6$

So, $2{B}_{0} - 6 ( - 6 ) = 20$

$2{B}_{0} = 20 - 36 ⇒ {B}_{0} = - 8$

∴ \overset{\to}{B} = - 6\overset{^}{ı} - 6\overset{^}{ȷ} - 8\overset{^}{k}