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Home Question Bank Math Geometry Archive 2024 November 30

Geometry Questions from Nov 30,2024

Browse the Geometry Q&A Archive for Nov 30,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Encuentre todos los valores de \( a \) tales que los vectores \( \bar{u}=(a, 2,4) \) y \( \bar{v}=(3,1,2) \bar{w}=(4,5, a) \mathrm{se} \) coplanares cuando se colocan de modo tal que sus puntos iniciales coinciden. Q1. Sketch and describe the following surfaces. \( \begin{array}{llll}\text { (a) } x+y+2 z=4 & \text { (b) } 4 x^{2}+y^{2}=16 & \text { (c) } 4 x^{2}+y^{2}-z^{2}=1 & \text { (d) } z=x\end{array} \) Considere los siguientes vectores: \[ u=(2,-1,1), \quad v=(1,2,-3) \quad \text { y } \quad w=(3, a, 5) \] Según la información, el valor del parámetro " \( a \) ", para el cual los tres vectores pertenecen al mismo plano, corresponde a: El valor del parámetro " \( a \) " corresponde a: Exercice 01 On considére les points suivants \( A(5 ; 7), B(2 ; 3) \) et \( C(9 ; 4) \). 1) Déterminer les coordonnés des vecteurs suivants : \( \overrightarrow{A B}, \overrightarrow{A C} \) et \( \overrightarrow{B C} \). 2) Calculer \( \overrightarrow{A B} \cdot \overrightarrow{A C} \) et det \( (\overrightarrow{A B} ; \overrightarrow{A C}) \). 3) Déduire la nature du triangle \( A B C \). 4) Calculer \( \cos (\overrightarrow{B A} ; \overrightarrow{B C}) \) et \( \operatorname{sinn}(\overrightarrow{C A} ; \overrightarrow{C B}) \). Exercice 02 1) On considerre les points \( A(7 ; 4), B(-2 ; 1), C(1 ;-2) \) a) Vérifier que \( \vec{n}(1 ; 3) \) est un vecteur normal à \( (A B) \) b) Déterminer une équation cartésienne de la droite \( (A B) \) 2) Déterminer une équation cartésienne de la droite \( (D) \) Passant par \( C \) et perpendiculaire à la droite \( (A B) \) 3) Déterminer une équation cartésienne de la droite \( \left(D^{\prime}\right) \) la médiatrice du segment [BC]. Exercice 03 Dada la ecuación simétrica de la recta \( l \), dada por: \[ l: \frac{1-x}{4}=\frac{y-2}{3}=\frac{2-z}{4} \] Determine el punto de intersección con el plano \( Y Z \). De acuerdo con lo anterior, el punto de intersección corresponde a Piramide \( v=\frac{1}{3} b \cdot h \) A line contains the points \( (-4,1) \) and \( (4,6) \). Decide whether or not each of these poin is also on the line: \( \begin{array}{ll}\text { a. }(0,3.5) & \text { b. }(12,11) \\ \text { c. }(80,50) & \text { d. }(-1,2.875)\end{array} \) A rectangular parking lot is 20 ft longer than it is wide. Find the dimensions of the parking lot if it measures 100 ft diagonally If line segment AB is a chord of a circle and CD is the perpendicular bisector of AB, explain how you would determine the radius of the circle knowing the distance from the center to line AB. volumen de las prismo \( v=a \cdot b \cdot c \)
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