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

The direction cosines of the vector $3\hat{i} - 4\hat{j} + 5\hat{k}$ are

The projections of a vector on the three coordinate axes are $6, -3, 2$ respectively. The direction cosines of the vector are:

The vectors $a$,$b$,and $a + b$ are:

If $O$ is the origin and the position vector of $A$ is $4\,i + 5\,j$,then a unit vector parallel to $\overrightarrow{OA}$ is:

Let $\vec{a}, \vec{b}, \vec{c}$ be three non-zero vectors such that no two of them are collinear. If the vector $\vec{a} + 3\vec{b}$ is collinear with $\vec{c}$ and $\vec{b} + 2\vec{c}$ is collinear with $\vec{a}$,then find the value of $\vec{a} + 3\vec{b} + 6\vec{c}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module