If the origin is the orthocenter of an equila | vedclass

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(B) For an equilateral triangle,the orthocenter,circumcenter,centroid,and incenter all coincide at the same point. Given that the origin is the orthoc

Vedclass · Accepted Answer

$\vec{a}+\vec{b}=-\vec{c}$

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(B) For an equilateral triangle,the orthocenter,circumcenter,centroid,and incenter all coincide at the same point. Given that the origin is the orthocenter,it is also the centroid of the triangle. The centroid of a triangle with vertices $\vec{a}, \vec{b}, \vec{c}$ is given by $\frac{\vec{a}+\vec{b}+\vec{c}}{3}$. Since the centroid is the origin,we have: $\frac{\vec{a}+\vec{b}+\vec{c}}{3} = \vec{0}$ $\vec{a}+\vec{b}+\vec{c} = \vec{0}$ Therefore,$\vec{a}+\vec{b} = -\vec{c}$.

If the origin is the orthocenter of an equilateral triangle whose vertices are represented by the position vectors $\vec{a}, \vec{b}, \vec{c}$,then which of the following is true?

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