7. De las ciudades P, Q, R, S y T se sabe lo sigulente -La ciudad P se encuentra a 40 Km al sur de R, pero a 20 Km al oeste de S -La ciudad Q está a 20 Km al oeste de R y la ciudad T a 15 Km al sur de \( P \) De acuerdo con los datos ¿Cuál es la afirmación correcta? a) S está al sureste de Q b) P está al noreste de Q c) P estả la noreste de T d) Testá al noreste de Q e) R está al noreste de Q

Cho mặt phăng \( (\alpha) \) và đường thẳng \( d \not \subset(\alpha) \). Khẳng định nào sau đây là sa A. Nếu \( d / /(\alpha) \) thì trong \( (\alpha) \) tồn tại đường thẳng \( \Delta \) sao cho \( \Delta / / d \). B. Nếu \( d / /(\alpha) \) và \( b \subset(\alpha) \) thì \( b / / d \). C. Nếu \( d \cap(\alpha)=A \) và \( d^{\prime} \subset(\alpha) \) thì \( d \) và \( d^{\prime} \) hoặc cắt nhau hoặc chéo nha D. Nếu \( d / / c ; c \subset(\alpha) \) thì \( d / /(\alpha) \).

How can you determine the surface area of a cube using its net diagram? Describe the steps involved.

(c) The planes \( \Pi_{2} \) and \( \Pi_{3} \) are with equations \( \left.2 x+2 y+1\right) \) respectively, where \( p \) is a constant. (i) Find the vector equation of the line of intersection between planes \( \Pi_{1} \) and \( \Pi_{2} \). (ii) Determine the value of \( p \) such that the planes \( \Pi_{1}, \Pi_{2} \) and \( \Pi_{3} \) do not have any common point.

Given the equations of lines \( \boldsymbol{l}_{1} \) and \( \boldsymbol{l}_{2} \) are \( \mathrm{r}=(\mathrm{i}+2 \mathrm{j}+3 \mathrm{k})+\lambda(\mathrm{i}-\mathrm{j}+2 \mathrm{k}) \) and \( \mathrm{r}=(5 \mathrm{i}+\mathrm{j}+5 \mathrm{k})+\mu 2 \mathrm{i}+\mathrm{j}-2 \mathrm{k}) \) respectively, where \( \lambda \) and \( \mu \) are real patameters. (a) Show that lines \( \boldsymbol{\ell}_{1} \) and \( \boldsymbol{\ell}_{2} \) intersect and hence, state the coordinates of the point of intersection. (b) Find the Cartesian equation of the plane \( \Pi_{1} \), which contains lines \( \boldsymbol{\ell}_{1} \) and \( \boldsymbol{\ell}_{2} \). (c) The planes \( \Pi_{2} \) and \( \Pi_{3} \) are with equations \( 2 \mathrm{r}+2 \mathrm{y}+z=3 \) and \( 2 \mathrm{r}+p y+2 z=2 \) respectively, where \( p \) is a constant. (i) Find the vector equation of the line of intersection between planes \( \Pi_{1} \) and \( \Pi_{2} \). (ii) Determine the value of \( p \) such that the planes \( \Pi_{1}, \Pi_{2} \) and \( \Pi_{3} \) do not have any common point.

(27) If the distance between the point and the center of a circle \( =15 \mathrm{~cm} \). and the power of this point with respect to the circle \( =144 \mathrm{~cm}^{2} \), then the radius length of the circle \( =\ldots . . . . . . . \mathrm{cm} \). \( \begin{array}{llll}81 & \text { (b) } 9 & \text { (c) } \sqrt{963} & \text { (d) } 18\end{array} \)