Question

What is the cross product of (14i−7j−7k) and (−5i+12j+2k)?

Answer 1

$\begin{vmatrix}\hat{ i} &\hat{ j}&\hat{ k}\\14&-7&-7\\-5&12&2\end{vmatrix}$

$\Rightarrow \hat{ i} \begin{vmatrix} -7&-7\\12&2\end{vmatrix}-\hat{ j} \begin{vmatrix} 14&-7\\-5&2\end{vmatrix}+ \hat{ k} \begin{vmatrix}14&-7\\-5&12 \end{vmatrix}$

$\Rightarrow \hat{ i} \begin{vmatrix} -7&-7\\12&2\end{vmatrix}-\hat{ j} \begin{vmatrix} 14&-7\\-5&2\end{vmatrix}+ \hat{ k} \begin{vmatrix}14&-7\\-5&12 \end{vmatrix}$

$\Rightarrow \hat{ i} [-7 \times 2 - (-7 \times 12)] -\hat{ j} [14 \times 2 - (-7 \times -5)] + \hat { k} [14 \times 12 - (-7 \times -5)]$

$\Rightarrow \hat{ i}[-14 + 84] -\hat { j}[28 - 35] + \hat { k} [168 -35]$$\Rightarrow 70 \hat { i} - (-7) \hat { j} + 133 \hat{ k}$$\Rightarrow 70 \hat{ i} +7 \hat{ j} + 133 \hat {k}$