Q. Five points given by $A,B,C,D,E$ are in plane. Three forces $\overrightarrow{\mathbf{AC}}\mathbf{,\ }\overrightarrow{\mathbf{\ AD}}$ and $\overrightarrow{\mathbf{AE}}$ act a $A$ and three forces $\overrightarrow{\mathbf{CB}}\mathbf{,}\overrightarrow{\mathbf{DB}}\mathbf{,}\overrightarrow{\mathbf{EB}}$ act at $B$. Then, their resultant is
Explanation
(b)
All points $A,B,C,D,E$ are in a plane.
$\therefore$ Resultant $= \left( \mathbf{\ }\overrightarrow{\mathbf{AC}}\mathbf{+}\overrightarrow{\mathbf{AD}}\mathbf{+}\overrightarrow{\mathbf{AE}}\mathbf{\ } \right)\mathbf{+}\left( \mathbf{\ }\overrightarrow{\mathbf{CB}}\mathbf{+}\overrightarrow{\mathbf{DB}}\mathbf{+}\overrightarrow{\mathbf{EB}} \right)$
$= \left( \mathbf{\ }\overrightarrow{\mathbf{AC}}\mathbf{+}\overrightarrow{\mathbf{CB}}\mathbf{\ } \right)\mathbf{+}\left( \mathbf{\ }\overrightarrow{\mathbf{AD}}\mathbf{+}\overrightarrow{\mathbf{DB}}\mathbf{\ } \right)\mathbf{+}\left( \mathbf{\ }\overrightarrow{\mathbf{AE}}\mathbf{+}\overrightarrow{\mathbf{EB}}\mathbf{\ } \right)$
$= \overrightarrow{\mathbf{AB}}\mathbf{+}\overrightarrow{\mathbf{AB}}\mathbf{+}\overrightarrow{\mathbf{AB}}\mathbf{=}3\overrightarrow{\mathbf{AB}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.