Question

Five points given by A, B, C, D, E are in a plane. Three forces $\overset{\rightarrow}{AC},\overset{\rightarrow}{AD}$ and $\overset{\rightarrow}{AE}$ act at A and three forces $\overset{\rightarrow}{CB},\overset{\rightarrow}{DB},\overset{\rightarrow}{EB}$ act at B. Then their resultant is

• A. $2\overset{\rightarrow}{AC}$
• B. $3\overset{\rightarrow}{AB}$
• C. $3\overset{\rightarrow}{DB}$
• D. $2\overset{\rightarrow}{BC}$

Answer 1

Answer: (B)

$3\overset{\rightarrow}{AB}$

Answer 2

Points A, B, C, D, E are in a plane.

Resultant $= (\overset{\rightarrow}{AC} + \overset{\rightarrow}{AD} + \overset{\rightarrow}{AE}) + (\overset{\rightarrow}{CB} + \overset{\rightarrow}{DB} + \overset{\rightarrow}{EB})$

$= (\overset{\rightarrow}{AC} + \overset{\rightarrow}{CB}) + (\overset{\rightarrow}{AD} + \overset{\rightarrow}{DB}) + (\overset{\rightarrow}{AE} + \overset{\rightarrow}{EB})$

$= \overset{\rightarrow}{AB} + \overset{\rightarrow}{AB} + \overset{\rightarrow}{AB} = 3\overset{\rightarrow}{AB}$.