Find the centroid of a triangle having vertices A(1, 2, 3), B(- 1, 0, 0) and C(3, 7, 6)?

Concept:

Centroid of a triangle:

If the three vertices of the triangle are A(x1, y1), B(x2, y2), C(x3, y3) then the centroid of a triangle = \(\rm (\frac{x_{1}+x_{2}+x_{3}}{3}, \frac{y_{1}+y_{2}+y_{3}}{3}).\)

Calculation:

Given: A(1, 2, 3), B(- 1, 0, 0) and C(3, 7, 6)

As we know that, if A(x1, y1), B(x2, y2), C(x3, y3) are the vertices of a triangle then the centroid of the triangle is given by: \(\rm (\frac{x_{1}+x_{2}+x_{3}}{3}, \frac{y_{1}+y_{2}+y_{3}}{3}, \frac{z_{1}+z_{2}+z_{3}}{3}).\)

Let the centroid of the triangle be R.

\(\Rightarrow \rm R=(\frac{1-1+3}{3}, \frac{2+0+7}{3} ,\frac{3+0+6}{3} )=(1, 3, 3)\)

Hence, the correct option is 4.