If the origin is the orthocenter of an equila | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

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

Vedclass · Answer

(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?

Similar Questions

The vector in the direction of vector $5 \hat{i} - \hat{j} + 2 \hat{k}$ with a magnitude of $8$ units is:

If $O$ is the origin and $C$ is the midpoint of $A(2, -1)$ and $B(-4, 3)$,then the value of $\overrightarrow{OC}$ is:

$A$ unit vector in $XY$-plane making an angle $45^{\circ}$ with $\hat{i}+\hat{j}$ and an angle $60^{\circ}$ with $3\hat{i}-4\hat{j}$ is

The direction ratios of the line bisecting the angle between the $x$-axis and the line having direction ratios $(3, -1, 5)$ are

If $\bar{a}, \bar{b}, \bar{c}$ are non-zero vectors such that no two of them are parallel,and $\bar{a} + \bar{b}$ is parallel to $\bar{c}$,and $\bar{b} + \bar{c}$ is parallel to $\bar{a}$,then $\bar{a} + \bar{b} + \bar{c} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module