dados os vetores u=(2,-1,1); v=(1,-1,0) e w=(-1,2,2) determine (u+v) x (u-v)

PAra determinarmos a expressão dada, devemos realizar os cálculos abaixo:

\(\begin{align} & u(2,-1,1) \\ & v(1,-1,0) \\ & w(-1,2,2) \\ & \\ & u+v=(2,-1,1)+(1,-1,0) \\ & u+v=(3,-2,1) \\ & \\ & u-v=(2,-1,1)-(1,-1,0) \\ & u-v=(1,0,1) \\ & \\ & \left( u-v \right)\times \left( u+v \right)=\left[ \begin{matrix} i & j & k \\ 3 & -2 & 1 \\ 1 & 0 & 1 \\ \end{matrix} \right] \\ & \left( u-v \right)\times \left( u+v \right)=\det \left[ \begin{matrix} i & j & k \\ 3 & -2 & 1 \\ 1 & 0 & 1 \\ \end{matrix} \right]\begin{matrix} i & j \\ 3 & -2 \\ 1 & 0 \\ \end{matrix} \\ & \left( u-v \right)\times \left( u+v \right)=-2i+j+2k-3j \\ & \left( u-v \right)\times \left( u+v \right)=-2i-2j+2k \\ \end{align}\ \)

=(-3 6 6)

Segundo a calculadora cientifica!