\( \left\{\begin{array}{l}\text { a) El plano: } \pi:(x ; y ; z)=\alpha(1 ; 0 ;-1)+\beta(0 ; 1 ; 2)+(0 ; 0 ; 2) \text { y la recta } r:(x ; y ; z)=\lambda(2 ; 1 ; 0)+ \\ (2 ; 1 ; 2) \text { son perpendiculares. } \\ \text { b) Dados dos vectores perpendiculares } \vec{u} \text { y } \vec{w} \text {, se sabe que satisfacen: }\|\vec{w}\|=2\|\vec{u}\| \text {, entonces } \\ (3 \vec{u}+3 \vec{w}) \cdot(-v \vec{w}+4 \vec{u})=0\end{array}\right. \)

7. En cada ítem, estudiar la posición relativa entre las dos rectas dadas y graficar ambas en un mismo sistema de coordenadas cartesianas. a) \( \left\{\begin{array}{l}x=1-5 \lambda \\ y=2+3 \lambda \\ z=-5+\lambda\end{array}\left\{\begin{array}{l}x=1 \\ y=1 \\ z=\mu\end{array}(\lambda, \mu \in \mathbb{R})\right.\right. \) b) \( \left\{\begin{array}{l}x=3+2 \alpha \\ y=1-\alpha \\ z=5\end{array}\left\{\begin{array}{l}x=-1-6 \beta \\ y=3+3 \beta \\ z=5\end{array} \quad(\alpha, \beta \in \mathbb{R})\right.\right. \)

\[ g: \vec{x}=\left(\begin{array}{l}3 \\ 1 \\ 4\end{array}\right)+t\left(\begin{array}{c}2 \\ -7 \\ 5\end{array}\right) \quad h: \vec{x}=\left(\begin{array}{c}5 \\ -6 \\ 9\end{array}\right)+k\left(\begin{array}{l}1 \\ 1 \\ 1\end{array}\right) \] (1) Zeigen Sie, das die Geraden sich schneiden. (2) Geben Sie den Schnittpunkt an. (3) Prüfen Sie, ob sie senkrecht aufeinander stehen. b) Formulieren Sie in mathematischer Schreibweise mithilfe des

555. Длина прямоугольника \( 7 \frac{3}{5} \) см. Его периметр равен периме квадрата со стороной 6 см. Найдите ширину прямоуго ника.

What is the formula for calculating the volume of a cone?

The cylindrical sleeve shown above was made according to all the specifications on its drawing. However, it is found to be off- center. What type of geometric tolerance might this part fall outside of?Concentricity Cylindricity Straightness Limit Angularity