Question

A, B, C, D, E are five coplanar points, then

$\overset{\rightarrow}{DA} + \overset{\rightarrow}{DB} + \overset{\rightarrow}{DC} + \overset{\rightarrow}{AE} + \overset{\rightarrow}{BE} + \overset{\rightarrow}{CE}$ is equal to

• A. $\overset{\rightarrow}{DE}$
• B. $3\overset{\rightarrow}{DE}$
• C. $2\overset{\rightarrow}{DE}$
• D. $4\overset{\rightarrow}{ED}$

Answer 1

Answer: (B)

$3\overset{\rightarrow}{DE}$

Answer 2

$A,B,C,D,E$ are five co-planar points.

$\overset{\rightarrow}{DA} + \overset{\rightarrow}{DB} + \overset{\rightarrow}{DC} + \overset{\rightarrow}{AE} + \overset{\rightarrow}{BE} + \overset{\rightarrow}{CE}$

=$(\overset{\rightarrow}{DA} + \overset{\rightarrow}{AE}) + (\overset{\rightarrow}{DB} + \overset{\rightarrow}{BE}) + (\overset{\rightarrow}{DC} + \overset{\rightarrow}{CE})$

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