The position vector of the point of intersect | vedclass

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

Question

(A) The centroid $G$ of a triangle with vertices $A(x_1, y_1, z_1)$,$B(x_2, y_2, z_2)$,and $C(x_3, y_3, z_3)$ is given by the formula:$G = \left( \fra

Vedclass · Accepted Answer

$2 \hat{i} + \hat{j} + \hat{k}$

Vedclass · Answer

(A) The centroid $G$ of a triangle with vertices $A(x_1, y_1, z_1)$,$B(x_2, y_2, z_2)$,and $C(x_3, y_3, z_3)$ is given by the formula:$G = \left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}, \frac{z_1 + z_2 + z_3}{3} \right)$Given vertices are $A(1, 2, 3)$,$B(1, 0, 3)$,and $C(4, 1, -3)$.Substituting the values:$G = \left( \frac{1 + 1 + 4}{3}, \frac{2 + 0 + 1}{3}, \frac{3 + 3 - 3}{3} \right)$$G = \left( \frac{6}{3}, \frac{3}{3}, \frac{3}{3} \right)$$G = (2, 1, 1)$The position vector of the centroid is $2 \hat{i} + \hat{j} + \hat{k}$.

The position vector of the point of intersection of the medians (centroid) of a triangle,whose vertices are $A(1, 2, 3)$,$B(1, 0, 3)$,and $C(4, 1, -3)$ is

Similar Questions

If $C$ is the mid-point of the line segment $AB$ and $P$ is any point outside the line $AB$,then

If $|\overline{a}|=2, |\overline{b}|=3, |\overline{c}|=5$ and each of the angles between the vectors $\overline{a}$ and $\overline{b}$,$\overline{b}$ and $\overline{c}$,and $\overline{c}$ and $\overline{a}$ is $60^{\circ}$,then the value of $|\overline{a}+\overline{b}+\overline{c}|$ is

Let $\vec{a}, \vec{b}, \vec{c}$ be three non-coplanar vectors. Then the point of intersection of the line joining the points $\vec{a}+\vec{b}+\vec{c}, \vec{a}-\vec{b}+3 \vec{c}$ and the line joining the points $2 \vec{a}-\vec{b}+\vec{c}, \vec{a}-2 \vec{b}+4 \vec{c}$ is

Find the position vector of the midpoint of the vector joining the points $P(2, 3, 4)$ and $Q(4, 1, -2)$.

Find the vector joining the points $P(2, 3, 0)$ and $Q(-1, -2, -4)$ directed from $P$ to $Q$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module