Question

3. Dados os vetores u (3,2, -1), v = (0,2,-3) e w = (1,-1,0), calcule: (v xu) x w​

Answer 1

Resposta:

($\overrightarrow{v}$ x $\overrightarrow{u}$) x $\overrightarrow{w}$ = (-6, -6, 5)

Explicação passo a passo:

→ $\overrightarrow{v}$ x $\overrightarrow{u}$ = (0, 2, -3) x (3, 2, -1) =

= $\left|\begin{array}{ccc}\overrightarrow{i}&\overrightarrow{j}&\overrightarrow{k}\\0&2&-3\\3&2&-1\end{array}\right|=-2\overrightarrow{i}-9\overrightarrow{j}-6\overrightarrow{k}+6\overrightarrow{i}=4\overrightarrow{i}-9\overrightarrow{j}-6\overrightarrow{k}=(4,-9,-6)$

→ ($\overrightarrow{v}$ x $\overrightarrow{u}$) x $\overrightarrow{w}$ = (4, -9, -6) x (1, -1, 0) =

= $\left|\begin{array}{ccc}\overrightarrow{i}&\overrightarrow{j}&\overrightarrow{k}\\4&-9&-6\\1&-1&0\end{array}\right|=-6\overrightarrow{j}-4\overrightarrow{k}+9\overrightarrow{k}-6\overrightarrow{i}=-6\overrightarrow{i}-6\overrightarrow{j}+5\overrightarrow{k}=(-6,-6,5)$