Question

Find the vector from the origin O to the centroid of the triangle whose vertices are (1, -1, 2), (2, 1, 3) and (-1, 2, -1).

Answer 1

Centeroid of the triangle with Vertices (x₁, y₁, z₁), (x₂, y₂, z₂), and (x₃, y₃, z₃) is given by,

In vector algebra, ‘x’ consider as a coefficient of \(\hat i\) and ‘y’ as a coefficient of  \(\hat j\)  and ‘z’ as a coefficient of  \(\hat k\)  So the position vector of the centroid,

So the location of the centroid is

And the vector is,