Question

If $\overrightarrow{A}=2\overrightarrow{i}+3\overrightarrow{j}+4\overrightarrow{k}\mathrm{and}\overrightarrow{B}=4\overrightarrow{i}+3\overrightarrow{j}+2\overrightarrow{k}$, find $\overrightarrow{\mathrm{A}}\times \overrightarrow{\mathrm{B}}$.

Answer 1

Given: $\overrightarrow{\mathit{A}}\mathit{=}2\hat{\mathit{i}}\mathit{+}3\hat{\mathit{j}}\mathit{+}4\hat{\mathit{k}}\mathit{}$and $\overrightarrow{\mathit{B}}\mathit{=}4\hat{\mathit{i}}\mathit{+}3\hat{\mathit{j}}\mathit{+}2\hat{\mathit{k}}$
The vector product of $\overrightarrow{\mathit{A}}\mathit{\times }\overrightarrow{\mathit{B}}$ can be obtained as follows:
$$\begin{gathered} \overrightarrow{A}\mathit{\times }\overrightarrow{B}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 2& 3& 4\\ 4& 3& 2\end{array}\right| \\ =\hat{i}\left(6-12\right)-\hat{j}\left(4-16\right)+\hat{k}\left(6-12\right) \\ =-6\hat{i}+12\hat{j}-6\hat{k} \end{gathered}$$