1. **Problem:** Given two vectors $\vec{a} = (1, 2, -1)$ and $\vec{b} = (3, 0, 2)$ in space $Oxyz$, find the coordinates of the cross product vector $[\vec{a}, \vec{b}]$. 2. **Formula:** The cross product of two vectors $\vec{a} = (a_1, a_2, a_3)$ and $\vec{b} = (b_1, b_2, b_3)$ is given by: $$ [\vec{a}, \vec{b}] = \left(a_2 b_3 - a_3 b_2, a_3 b_1 - a_1 b_3, a_1 b_2 - a_2 b_1\right) $$ This vector is perpendicular to both $\vec{a}$ and $\vec{b}$. 3. **Calculate each component:** - First component: $$ 1st = 2 \times 2 - (-1) \times 0 = 4 - 0 = 4 $$ - Second component: $$ 2nd = (-1) \times 3 - 1 \times 2 = -3 - 2 = -5 $$ - Third component: $$ 3rd = 1 \times 0 - 2 \times 3 = 0 - 6 = -6 $$ 4. **Result:** $$ [\vec{a}, \vec{b}] = (4, -5, -6) $$ 5. **Answer:** The coordinates of the cross product vector are $(4; -5; -6)$, which corresponds to options A and B. Since options A and B are the same, the correct answer is $(4; -5; -6)$.