A) \[\vec{a}+\vec{b}+\vec{c}=\vec{0}\]
B) \[\vec{a}+\vec{b}+\vec{c}=\,\,unit\,\,vector\]
C) \[\vec{a}+\vec{b}=\vec{c}\]
D) \[\vec{a}=\vec{b}+\vec{c}\]
Correct Answer: A
Solution :
[a] Position vectors of vertices A, B and C are \[\overset{\to }{\mathop{a}}\,,\overset{\to }{\mathop{b}}\,\] and \[\overset{\to }{\mathop{c}}\,\]. \[\because \] triangle is equilateral. \[\therefore \] Centroid and orthocenter will coincide. Centroid \[\equiv \] orthocenter position vector \[=\frac{1}{3}(\overset{\to }{\mathop{a}}\,+\overset{\to }{\mathop{b}}\,+\overset{\to }{\mathop{c}}\,)\] \[\because \] given in question orthocenter is at origin. Hence \[\frac{1}{3}(\overset{\to }{\mathop{a}}\,+\overset{\to }{\mathop{b}}\,+\overset{\to }{\mathop{c}}\,)=0\] \[\overset{\to }{\mathop{a}}\,+\overset{\to }{\mathop{b}}\,+\overset{\to }{\mathop{c}}\,=0\]You need to login to perform this action.
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