A) A zero vector
B) A unit vector
C) 0
D) None of these
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, \[\overrightarrow{AD}+\overrightarrow{BE}+\overrightarrow{CF}\] \[=\frac{\mathbf{b}+\mathbf{c}-2\mathbf{a}}{2}+\frac{\mathbf{c}+\mathbf{a}-2\mathbf{b}}{2}+\frac{\mathbf{a}+\mathbf{b}-2\mathbf{c}}{2}=\mathbf{0}\].You need to login to perform this action.
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