Vector Algebra Question 232
Question: If D, E, F be the middle points of the sides BC, CA and AB of the triangle ABC, then $ \overrightarrow{AD}+\overrightarrow{BE}+\overrightarrow{CF} $ is
Options:
A) A zero vector
B) A unit vector
C) 0
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
- $ \overrightarrow{AD}=\overrightarrow{OD}-\overrightarrow{OA}=\frac{\mathbf{b}+\mathbf{c}}{2}-\mathbf{a}=\frac{\mathbf{b}+\mathbf{c}-2\mathbf{a}}{2} $ , (where $ O $ is the origin for reference) Similarly, $ \overrightarrow{BE}=\overrightarrow{OE}-\overrightarrow{OB}=\frac{\mathbf{c}+\mathbf{a}}{2}-\mathbf{b}=\frac{\mathbf{c}+\mathbf{a}-2\mathbf{b}}{2} $ and $ \overrightarrow{CF}=\frac{\mathbf{a}+\mathbf{b}-2\mathbf{c}}{2} $ . Now, $ \overrightarrow{AD}+\overrightarrow{BE}+\overrightarrow{CF} $ $ =\frac{\mathbf{b}+\mathbf{c}-2\mathbf{a}}{2}+\frac{\mathbf{c}+\mathbf{a}-2\mathbf{b}}{2}+\frac{\mathbf{a}+\mathbf{b}-2\mathbf{c}}{2}=\mathbf{0} $ .
BETA
