Internal section formula in 3D for JEE

Formula

\(R\left(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n},\frac{mz_2+nz_1}{m+n}\right)\)

Variables: \(R\) divides the segment joining \(P(x_1,y_1,z_1)\) and \(Q(x_2,y_2,z_2)\) internally in the ratio \(m:n\), i.e. \(PR:RQ=m:n\).

Conditions: \(m,n>0\), \(m+n\neq 0\).

Finding points dividing a segment in a given ratio, medians and centroid type problems.