A) \[\overrightarrow{0}\]
B) \[-\left( \frac{\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}}{2} \right)\]
C) \[\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}\]
D) \[\left( \frac{\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}}{2} \right)\]
Correct Answer: D
Solution :
Position vector of the centroid of \[\Delta ABC\] is \[=\left( \frac{\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}}{3} \right)\] Now we known that centroid divides the line joining orthocenter to circum centre divided by centriod divided by centroid in the ratio in 2 : 1orthocenter\[=3\left( \frac{\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}}{3} \right)-2\left( \frac{\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}}{4} \right)=\left( \frac{\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}}{2} \right)\]You need to login to perform this action.
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