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Question: ABCDE is a pentagon. Forces \(\overset{\rightarrow}{AB},\overset{\rightarrow}{AE},\overset{\rightarr...

ABCDE is a pentagon. Forces AB→,AE→,DC→,ED→\overset{\rightarrow}{AB},\overset{\rightarrow}{AE},\overset{\rightarrow}{DC},\overset{\rightarrow}{ED} act at a point. Which force should be added to this system to make the resultant cos⁡−145\cos^{- 1}\frac{4}{5}

A

AC→\overset{\rightarrow}{AC}

B

AD→\overset{\rightarrow}{AD}

C

BC→\overset{\rightarrow}{BC}

D

BD→\overset{\rightarrow}{BD}

Answer

BC→\overset{\rightarrow}{BC}

Explanation

Solution

AE→+ED→+DC→+AB→=AD→+DC→+AB→=AC→+AB→.\overset{\rightarrow}{AE} + \overset{\rightarrow}{ED} + \overset{\rightarrow}{DC} + \overset{\rightarrow}{AB} = \overset{\rightarrow}{AD} + \overset{\rightarrow}{DC} + \overset{\rightarrow}{AB} = \overset{\rightarrow}{AC} + \overset{\rightarrow}{AB}.

Obviously, if BC→\overset{\rightarrow}{BC} is added to this system, then it will be AC→+AB→+BC→=AC→+AC→=2AC→.\overset{\rightarrow}{AC} + \overset{\rightarrow}{AB} + \overset{\rightarrow}{BC} = \overset{\rightarrow}{AC} + \overset{\rightarrow}{AC} = 2\overset{\rightarrow}{AC}.