Question

The position vectors of the four angular point of a tetrahedron $OABC$ are $(0,0,0)$; $(0,0,2)$; $(0,4,0)$ and $(6,0,0)$ respectively. Find the coordinates of cenroid

• A. $(2,\frac{4}{3},\frac{2}{3})$
• B. $\left(\frac{6}{4},1,\frac{2}{4}\right)$
• C. $(0,0,0)$
• D. none of these

Answer 1

The correct option is B $\left(\frac{6}{4},1,\frac{2}{4}\right)$

Angular points of tetrahedron OABC are $(0,0,0),(0,0,2),(0,4,0),(6,0,0)$

To find the coordinates of the centroid of the tetrahedron whose vertices are $(x_1,y_1,z_1),(x_2,y_2,z_2),(x_3,y_3,z_3)$ and $(x_4,y_4,z_4).$

Hence, the centroid is

$\left(\frac{x_1+x_2+x_3+x_4}{4}\right),\left(\frac{y_1+y_2+y_3+y_4}{4}\right),\left(\frac{z_1+z_2+z_3+z_4}{4}\right)$

Now, substituting the values we get

$\left(\frac{0+0+0+6}{4}\right),\left(\frac{0+0+4+0}{4}\right),\left(\frac{0+2+0+0}{4}\right)$

$\therefore$ the coordinates of the centroid are : $(\frac{6}{4},1,\frac{2}{4})$