Exercice 2 Dans un repere orthonorme \( (O, \vec{i}, j) \) on considére les points \( A(-2,1) ; B(0 ;-2) ; C(1 ; 3) \). 1) Calculer \( A B ; A C ; B C \) et \( \overline{A B} \cdot \overline{A C} \) 2) Déduire la nature du triangle \( A B C \) 3) Calculer la surface ditriangle \( A B C \) 4) Calculer \( \overline{B C} \cdot \overline{B A} ; \cos (\overline{B C} ; \overline{B A}) ; \sin (\overline{B C} ; \overline{B A}) \) et dedduire la mesure principale de l'angle \( (\overline{B C} ; \overline{B A}) \)

Find the center and radius of the circle represented by the equation below. \[ (x-4)^{2}+(y-8)^{2}=25 \] Answer Attempt 1 out of 5 Center: \( (\square, \square \) Radius:

Use the given vectors to find \( \mathbf{v} \cdot \mathbf{w} \) and \( \mathbf{v} \cdot \mathbf{v} \). \[ \begin{array}{l}\mathbf{v}=-7 \mathbf{i}-3 \mathbf{j}, \mathbf{w}=-9 \mathbf{i}-5 \mathbf{j} \\ \mathbf{v} \cdot \mathbf{w}=78 \text { (Simplify your answer.) } \\ \mathbf{v} \cdot \mathbf{v}=\square \text { (Simplify your answer.) }\end{array} \text { \$ } \]

(a) Find the dot product \( \mathbf{v} \cdot \mathbf{w} \); (b) find the angle between \( \mathbf{v} \) and \( \mathbf{w} \); (c) state whether the vectors are parallel, orthogonal, or neither. \( \mathbf{v}=\sqrt{3} \mathbf{i}+3 \mathbf{j}, \quad \mathbf{w}=-\mathbf{i}+\mathbf{j} \) (a) \( \mathbf{v} \cdot \mathbf{w}=3-\sqrt{3} \) (Simplify your answer. Type an exact answer, using radicals as needed.) (b) The angle between \( \mathbf{v} \) and \( \mathbf{w} \) is \( \square^{\circ} \). (Type your answer in degrees.)

Find the center and radius of the circle represented by the equation below. \[ (x-10)^{2}+(y-9)^{2}=256 \] Answer Attempt 1 out of 5 Center: Radius:

Determina la pendiente de la línea que pasa por los puntos \( (-1, -1) \) y \( (2, 5) \).