calcular a area do triagulo ABC,sendo (A-b)=(-1,13) e(B-C)=(-1,1,0)

vdd

Para encontrarmos a área do triângulo, realizaremos os cálculos abaixo:

\(\begin{align} & \left( A-b \right)=\left( -1,1,3 \right)\text{ } \\ & \left( B-C \right)=\left( -1,1,0 \right) \\ & \\ & A=\frac{1}{2}\cdot \left| AB\times AC \right| \\ & A=\frac{1}{2}\cdot \left[ \begin{matrix} i & j & k \\ -1 & 1 & 3 \\ -1 & 1 & 0 \\ \end{matrix} \right] \\ & A=\frac{1}{2}\cdot \det \left[ \begin{matrix} i & j & k \\ -1 & 1 & 3 \\ -1 & 1 & 0 \\ \end{matrix} \right]\begin{matrix} i & j \\ -1 & 1 \\ -1 & 1 \\ \end{matrix} \\ & A=\frac{1}{2}\cdot \left[ \left( -3j-k \right)+k-3i \right] \\ & A=\frac{1}{2}\cdot \left| -3i-3j \right| \\ & A=\frac{1}{2}\cdot \left| \sqrt{{{3}^{2}}+{{3}^{2}}} \right| \\ & A=\frac{\sqrt{18}}{2} \\ & A=\frac{3\sqrt{2}}{2} \\ \end{align}\ \)