Mathematics

The centroid of a tetrahedron is the average of its four vertices' coordinates. Since one vertex is the origin O(0, 0, 0) and the centroid is given, you can set up three equations by equating each coordinate of the centroid formula to its known value. This gives you the values of $a$, $b$, and $c$, which you then use to find the distance from the origin to the point $(a, b, c)$ and match it to the form $5\sqrt{\lambda}$.

The centroid of a tetrahedron is the average of its four vertices' coordinates. Since one vertex is the origin O(0, 0, 0) and the centroid is given, you can set up three equations by equating each coordinate of the centroid formula to its known value. This gives you the values of $a$, $b$, and $c$, which you then use to find the distance from the origin to the point $(a, b, c)$ and match it to the form $5\sqrt{\lambda}$.