Vector Algebra Question 258
Question: ABCDE is a pentagon. Forces $ \overrightarrow{AB},,\overrightarrow{AE},,\overrightarrow{DC},,\overrightarrow{ED} $ act at a point. Which force should be added to this system to make the resultant $ {{\cos }^{-1}}\frac{4}{5} $
[MNR 1984]
Options:
A) $ \overrightarrow{AC} $
B) $ \overrightarrow{AD} $
C) $ \overrightarrow{BC} $
D) $ \overrightarrow{BD} $
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Answer:
Correct Answer: C
Solution:
- $ \overrightarrow{AE}+\overrightarrow{ED}+\overrightarrow{DC}+\overrightarrow{AB}=\overrightarrow{AD}+\overrightarrow{DC}+\overrightarrow{AB} $ $ =\overrightarrow{AC}+\overrightarrow{AB}. $ Obviously, if $ \overrightarrow{BC} $ is added to this system, then it will be $ \overrightarrow{AC}+\overrightarrow{AB}+\overrightarrow{BC}=\overrightarrow{AC}+\overrightarrow{AC}=2\overrightarrow{AC}. $
BETA
