A) \[\vec{0}\]
B) \[\vec{A}+\vec{B}+\vec{C}\]
C) \[\frac{\vec{a}+\vec{b}+\vec{c}}{3}\]
D) \[\frac{\vec{a}-\vec{b}-\vec{c}}{3}\]
Correct Answer: A
Solution :
Position vectors of vertices A, B and C of the triangle \[ABC=\vec{a},\vec{b},\vec{c}\] Position vector of centroid of the triangle \[G=\frac{\vec{a}+\vec{b}+\vec{c}}{3}\]therefore, \[G\vec{A}+G\vec{B}+G\vec{C}=\left[ \vec{a}-\frac{(\vec{a}+\vec{b}+\vec{c})}{3} \right]\] \[+\left[ \vec{b}-\frac{(\vec{a}+\vec{b}+\vec{c})}{3} \right]\] \[+\left[ \vec{c}-\frac{(\vec{a}+\vec{b}+\vec{c})}{3} \right]\] \[=\frac{1}{3}[2\vec{a}-\vec{b}-\vec{c}+2\vec{c}-\vec{a}-\vec{b}]\] \[=0\]You need to login to perform this action.
You will be redirected in
3 sec