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 $\hat{i}, \hat{j}, \hat{k}$ are unit vectors,then which of the following is true?

Let $ABC$ be a triangle whose circumcentre is at $P$. If the position vectors of $A, B, C$ and $P$ are $\vec{a}, \vec{b}, \vec{c}$ and $\frac{\vec{a} + \vec{b} + \vec{c}}{4}$ respectively,then the position vector of the orthocentre of this triangle is:

$I$. Two non-zero, non-collinear vectors are linearly independent.
$II$. Any three coplanar vectors are linearly dependent.
Which of the above statements is/are true?

If $a$ and $b$ represent two non-collinear vectors, the equation $r = ta + (1-t)b$ represents

The points whose position vectors are $2\hat{i}+3\hat{j}+4\hat{k}$, $3\hat{i}+4\hat{j}+2\hat{k}$, and $4\hat{i}+2\hat{j}+3\hat{k}$ are the vertices of

Vedclass Test Series

Exam Paper Generator

Online Exam Module