piano e retta non sono paralleli, allora la richiesta è impossibile. EsERCIzio 12.10 Scrivere le equazioni cartesiane e parametriche del piano \( \pi \) passante per i punti \( P=(1,1,1) \) e \( Q=(2,1,2) \) e parallelo alla retta \( r:\left\{\begin{array}{l}x=t \\ y=-1-3 t \\ z=4-2 t\end{array}\right. \) SVOLGIMENTO Ci servono il vettore \( \overrightarrow{P Q}=(1,0,1) \) e il vettore direzionale \( v_{r}=(1,-3-2) \).

Find the equation of line perpendicular to \( 5 x-3 y+4=0 \) that passes through the point \( (-4,1) \).

Find the perpendicular d \( x^{2}+y^{2}-8 x+2 y+8 \) Hence, find the shortest

Angles 3 and 5 are \( \square \) and \( m \angle 5 \) is \( (2 x+11)^{\circ} \).

BCD un carré et \( G= \) bary \( \{(A, 2) ;(B,-1) ;(C, 2) ;(D ; 1)\} \) oient \( I= \) bary \( \{(A, 2) ;(B,-1)\} \) et \( J= \) bary \( \{(C, 2) ;(D ; 1)\} \); Montrer que \( 2 \overrightarrow{G A}-\overrightarrow{G B}=\overrightarrow{G I} \) et \( 2 \overrightarrow{G C}+\overrightarrow{G D}=3 \overrightarrow{G j} \) En déduire que \( G=\operatorname{bary\{ }(I, 1) ;(1,3)\} \) Construire I et \( J \) puis \( G \) a) Vérifier que: \( \forall M \in(P): 2 \overrightarrow{M A}-\overrightarrow{M B}+2 \overrightarrow{M C}+\overrightarrow{M D}=4 \overrightarrow{M G} \) b) Déterminer l'ensemble des points M du plan \( (P) \) tel que : \[ \|2 \overrightarrow{M A}-\overrightarrow{M B}+2 \overrightarrow{M C}+\overrightarrow{M D}\|=4\|2 \overrightarrow{M A}-\overrightarrow{M B}\| \]

What results when a plane is parallel to the axis of a double-napped cone and passes through the vertex? point parabola two intersecting lines a single line