Question

Fie punctele A(2, -1 ) si B( -1, 3) . Sa se determine numerele reale a si b astfel incat vectorul AB=ai+bj

Answer 1

$A(2,-1) \text{ \c{s}i } B(-1,3). \text{ S\u{a} se determine numerele reale a \c{s}i b}} \\ \text{astfel \^{i}nc\^{a}t vectorul }\overrightarrow{AB}= a\vec{i}+b\vec{j}.\\ \\ \begin{array}{rcl} \overrightarrow{AB} &=& (x_{B}-x_{A})\vec{i}+(y_B-y_{A})\vec{j} \\ &=& (-1-2)\vec{i}+\big[3-(-1)\big]\vec{j} \\ &=& -3\vec{i}+ (3+1)\vec{j} \\ &=& -3\vec{i}+4\vec{j} \end{array}\\ \\ \Rightarrow \boxed{a = -3 \text{ \c{s}i } b = 4}$