Answer
$$
\begin{aligned}
& \mathbf{F}_R=\{6 \mathbf{i}+5 \mathbf{j}-5 \mathbf{k}\} \mathrm{kN} \\
& \left(\mathbf{M}_R\right)_O=\{2.5 \mathbf{i}-7 \mathbf{j}\} \mathrm{kN} \cdot \mathrm{m}
\end{aligned}
$$
Work Step by Step
Position Vectors. The required position vectors are
$$
\mathbf{r}_1=\{0.8 \mathbf{i}-1.2 \mathbf{k}\} \mathrm{m} \quad \mathbf{r}_2=\{-0.5 \mathbf{k}\} \mathrm{m}
$$
Equivalent Resultant Force And Couple Moment At Point $\boldsymbol{O}$.
$$
\begin{aligned}
& \mathbf{F}_R=\Sigma \mathbf{F} \\
& \mathbf{F}_R=\mathbf{F}_1+\mathbf{F}_2 \\
& =(8 \mathbf{i}-2 \mathbf{k})+(-2 \mathbf{i}+5 \mathbf{j}-3 \mathbf{k}) \\
& =\{6 \mathbf{i}+5 \mathbf{j}-5 \mathbf{k}\} \mathrm{kN} \\
& \left(\mathbf{M}_R\right)_O=\Sigma \mathbf{M}_O ; \quad\left(\mathbf{M}_R\right)_O=\mathbf{r}_1 \times \mathbf{F}_1+\mathbf{r}_2 \times \mathbf{F}_2 \\
& =\left|\begin{array}{ccc}
\mathbf{i} & \mathbf{j} & \mathbf{k} \\
0.8 & 0 & -1.2 \\
8 & 0 & -2
\end{array}\right|+\left|\begin{array}{ccc}
\mathbf{i} & \mathbf{j} & \mathbf{k} \\
0 & 0 & -0.5 \\
-2 & 5 & -3
\end{array}\right| \\
& =(-8 \mathbf{j})+(2.5 \mathbf{i}+\mathbf{j}) \\
& =\{2.5 \mathbf{i}-7 \mathbf{j}\} \mathrm{kN} \cdot \mathrm{m} \\
&
\end{aligned}
$$
