1. **State the problem:** Given vector $\overrightarrow{AB} = -7\mathbf{i} + 3\mathbf{j} + 8\mathbf{k}$ and point $A(-2, -3, 6)$, find the coordinates of point $B$. 2. **Recall the formula:** The vector from $A$ to $B$ is given by $$\overrightarrow{AB} = B - A = (x_B - x_A, y_B - y_A, z_B - z_A)$$ where $B = (x_B, y_B, z_B)$. 3. **Set up equations:** Using the components of $\overrightarrow{AB}$, $$x_B - (-2) = -7$$ $$y_B - (-3) = 3$$ $$z_B - 6 = 8$$ 4. **Solve for each coordinate:** $$x_B + 2 = -7 \implies x_B = -7 - 2 = -9$$ $$y_B + 3 = 3 \implies y_B = 3 - 3 = 0$$ $$z_B - 6 = 8 \implies z_B = 8 + 6 = 14$$ 5. **Final answer:** $$B = (-9, 0, 14)$$ This means point $B$ is located at coordinates $(-9, 0, 14)$.