Question

Considere os vetores a=(1,00 m)i + (2,00 m)j; b=(3,00 kg m/s²)i + (1,00 kg m/s²)j e c=(0,50 π rad)k. Calcule (axb)*c

Answer 1

Resposta:

-2,5π J

Explicação passo a passo:

$\displaystyle\\ (\vec{a} \times \vec{b} ).\vec{c} = [(1\vec{i}+2\vec{j}) \times(3\vec{i}+1\vec{j})].0,5\pi\vec{k}=\\\\\ [1.3(\vec{i} \times\vec{i})+1.1(\vec{i} \times\vec{j})+2.3(\vec{j} \times\vec{i})+2.1(\vec{j} \times\vec{j})].0,5\pi\vec{k}=\\\\\ [3(0)+1\vec{k}+6(-\vec{k}) +2(0)].0,5\pi\vec{k}=\\\\\ [1\vec{k}-6\vec{k}].0,5\pi\vec{k}=\\\\\ [-5\vec{k}].0,5\pi\vec{k}=\\\\-2,5\pi$

com relação as unidades:

[m] . [kg m/s²] . [rad] = [m] . [N] . [rad] =  ([J] ÷ [rad]) . [rad] = [J}