Question

Dau coroana!! Fie punctele A(1,2) B( -1, 5) si O originea sistemului de coordonate Aflati coordonatele punctului M stiind ca OA vectorial + 2OB vectorial = OM vectorial

Answer 1

$A(1,2); \quad B(-1,5); \quad O(0,0); \quad M(a,b); \\ \\ \overrightarrow{OA} + 2\overrightarrow{OB} = \overrightarrow{OM} \Rightarrow\\ \Rightarrow (x_A-x_O)i + (y_A-y_O)j + 2\cdot \Big((x_B-x_O)i + (y_B-y_O)j\Big) = \\ =(x_M-x_O)i + (y_M-y_O)j \Rightarrow \\ \\ \Rightarrow (1-0)i+(2-0)j + 2\cdot\Big((-1-0)i+(5-0)j\Big) = (a-0)i + (b-0)j = \\ \\ \Rightarrow i+2j+2\cdot (-i+5j) = ai+bj \Rightarrow i+2j-2i+10j = ai+bj \Rightarrow$

$\Rightarrow -i+12j = ai+bj \Rightarrow \left\{ \begin{array}{c} a = -1 \\ b=12 \end{array} \right |\Rightarrow \boxed{M(-1,12)}$