Question

15. Dados u ⃗= (1,1, 2) e v ⃗= (2, 3, 1) calcule u ⃗ x v ⃗.

Answer 1

Resposta:

| i j k |

| 1 1 2 | = uxv

| 2 3 1 |

ux v = i+4j+ 3k - 2k -6i -j = -5i -2j +k   uxv = ( -5, -2,1)

Explicação passo-a-passo:

Answer 2

Resposta:

$\vec{u}\times\vec{v}=-5\vec{i}+3\vec{j}+\vec{k}$

Explicação passo-a-passo:

$\displaystyle \vec{u}\times\vec{v}=determinante(det)=\left[\begin{array}{ccc}i&j&k\\1&1&2\\2&3&1\end{array}\right]\\\\\\det =(1.1-3.2)\vec{i}-(1.1-2.2)\vec{j}+(1.3-2.1)\vec{k}=(1-6)\vec{i}-(1-4)\vec{j}+(1)\vec{k}=-5\vec{i}+3\vec{j}+\vec{k}$