Question

AB vectorial * AC vectorial=5 A(1, 2), B(2, 5), C(3, m) m=?

Answer 1

$A(1, 2), ~B(2, 5), ~C(3, m) \\ \\ \overrightarrow{AB}\cdot \overrightarrow{AC} = 5 \\ \\ \Big[(2-1)\vec{}i+ (5-2)\vec{j}\Big] \cdot \Big[ (3-1)\vec{i} + (m-2)\vec{j}\Big] = 5 \\ \\ (\vec{i}+3\vec{j}) \cdot \Big[2\vec{i}+(m-2)\vec{j}\Big] = 5\\ \\ 2\cdot 1 + 3\cdot (m-2) = 5 \\ 3\cdot(m-2) = 5-2 \\ 3\cdot(m-2) = 3 \\ m-2 = 1 \\ m = 1+2 \\ \\\Rightarrow \boxed{m = 3}$