Question
If $\vec{\text{A}}=2\vec{\text{i}}+3\vec{\text{j}}+4\vec{\text{k}}$ and $\vec{\text{B}}=4\vec{\text{i}}+3\vec{\text{j}}+2\vec{\text{k}},$ find $\vec{\text{A}}\times\vec{\text{B}}.$
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Answer
$\vec{\text{A}}=2\hat{\text{i}}+3\hat{\text{j}}+4\hat{\text{k}},\vec{\text{B}}=4\hat{\text{i}}+3\hat{\text{j}}+2\hat{\text{k}}$$\vec{\text{A}}\times\vec{\text{B}}=\begin{vmatrix}\hat{\text{i}}&\hat{\text{j}}&\hat{\text{k}}\\2&3&4\\4&3&2\end{vmatrix}$
$\Rightarrow\hat{\text{i}}(6-12)-\hat{\text{j}}(4-16)+\hat{\text{k}}(6-12)=-6\hat{\text{i}}+12\hat{\text{j}}-6\hat{\text{k}}$
$\Rightarrow\hat{\text{i}}(6-12)-\hat{\text{j}}(4-16)+\hat{\text{k}}(6-12)=-6\hat{\text{i}}+12\hat{\text{j}}-6\hat{\text{k}}$
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