Question

Sejam os vetores u(1,1,0) e v(0,1,2), determine um vetor w do R^3 tais que |w|=1 e u×w=0 e tambem v×w=0

Answer 1

          $\vec{w}\parallel \vec{u}\otimes\vec{v}=\det\left(\begin{matrix} \^i&\^j&\^k\\ u_1&u_2&u_3\\ v_1&v_2&v_3\\ \end{matrix}\right)=\det\left(\begin{matrix} \^i&\^j&\^k\\ 1&1&0\\ 0&1&2\\ \end{matrix}\right)=(2,-2,1)\\ \\ \\ \vec{w}=\dfrac{1}{\|(2.-2.1)\|}(2.-2.1)\\ \\ \\ \vec{w}=\dfrac{1}{3}(2.-2.1)\\ \\ \\ \boxed{~\boxed{\vec{w}=\left(\dfrac{2}{3}.-\dfrac{2}{3}.\dfrac{1}{3}\right) }~}$