iran-konkur 2015 Q133

iran-konkur · Other · konkur-riazi_1394 Vectors 3D & Lines Section Division and Coordinate Computation
133. Points $O(0,0,0)$, $B(-1,2,4)$, $A(5,-4,1)$ are given, and $\overrightarrow{AM} = \dfrac{2}{3}\overrightarrow{AB}$ and $\overrightarrow{AB}$ are known. The value of $|\overrightarrow{OM}|$ is:
(2) $\sqrt{11}$(1) $\sqrt{10}$
(4) $\sqrt{14}$(3) $\sqrt{13}$
\textbf{133.} Points $O(0,0,0)$, $B(-1,2,4)$, $A(5,-4,1)$ are given, and $\overrightarrow{AM} = \dfrac{2}{3}\overrightarrow{AB}$ and $\overrightarrow{AB}$ are known. The value of $|\overrightarrow{OM}|$ is:

\begin{tabular}{ll}
(2) $\sqrt{11}$ & (1) $\sqrt{10}$ \\
(4) $\sqrt{14}$ & (3) $\sqrt{13}$
\end{tabular}