Vector Algebra Question 247
Question: If the vectors represented by the sides AB and BC of the regular hexagon ABCDEF be a and b, then the vector represented by $ \overrightarrow{AE} $ will be
Options:
A) $ 2,\mathbf{b}-\mathbf{a} $
B) $ \mathbf{b}-\mathbf{a} $
C) $ 2,\mathbf{a}-\mathbf{b} $
D) $ \mathbf{a}+\mathbf{b} $
Show Answer
Answer:
Correct Answer: A
Solution:
- As in figure $ \overrightarrow{AB}=\mathbf{a}, $ $ \overrightarrow{BC}=\mathbf{b}, $ so $ \overrightarrow{AD}=2\mathbf{b} $ and $ \overrightarrow{ED}=\mathbf{a} $ . Now, $ \overrightarrow{AE}+\overrightarrow{ED}=\overrightarrow{AD}\Rightarrow \overrightarrow{AE}=\overrightarrow{AD}-\overrightarrow{ED}=2\mathbf{b}-\mathbf{a}. $
BETA
