1. Problem 7 asks to find $l_\alpha$, $t_\beta$, and calculate $h_{\alpha\alpha'} - h_{\alpha\alpha}$. Given relationship: $$h_{\alpha\alpha'} - h_{\alpha\alpha}$$ This expression indicates the difference between two values associated with indices $\alpha$ and $\alpha'$. Without further numerical data, this represents a symbolic difference. 2. Problem 9 asks to find the intersection $\alpha \cap \beta$ using points $h_{\beta\phi}$ and $h_{\beta\alpha\alpha}$. Intersection $\alpha \cap \beta$ means the set of points common to both sets $\alpha$ and $\beta$. Points $h_{\beta\phi}$ and $h_{\beta\alpha\alpha}$ are likely vertices or intersection points of these sets. 3. Problem 8 asks for $A^{*}$ given $A$ and points $n^{*}$, $\alpha^{\prime\prime}$, $m^{\prime\prime}$, $A'$, $m'$, $\alpha'$ $A^{*}$ may represent a transformation or dual of $A$, possibly using these given points. 4. Problem 10 asks for $\alpha \cap m$ and $m$'s corresponding $q$ and $d$ elements. Points given: $m^{\prime\prime}$, $\alpha^{\prime\prime}$, $b^{\prime\prime}$, $a^{\prime\prime}$, $\alpha'$, $b'$, $m'$ Finding $\alpha \cap m$ means the intersection of these lines or sets. The $q$ and $d$ likely represent some parameters related to $m$. 5. Problem 11 asks for the point $A$ belonging to line $mL \alpha$ where $m = z$, points $A''$, $f_{\alpha\alpha''}$, $P_{\alpha\alpha''}$ are given. This requires confirming that $A$ lies on line $mL \alpha$ and finding $m$ based on these points. Final answers: - For 7: $$h_{\alpha\alpha'} - h_{\alpha\alpha}$$ (symbolic difference) - For 9: $$\alpha \cap \beta = \{h_{\beta\phi}, h_{\beta\alpha\alpha}\}$$ (the intersection points) - For 8: $$A^{*} = \{n^{*}, \alpha^{\prime\prime}, m^{\prime\prime}, A', m', \alpha'\}$$ (transformed set) - For 10: $$\alpha \cap m = \{m^{\prime\prime}, \alpha^{\prime\prime}, b^{\prime\prime}, a^{\prime\prime}, \alpha', b', m'\}$$ - For 11: $$A \in mL \alpha, \quad m = z$$ These represent the symbolic solutions based on given notation and points since no numeric data is provided.