The section formula determines the position vector of a point dividing a line segment. For internal division of segment AB in ratio m:n: p = $\frac{m**b** + n**a**}{(m+n)}$. For external division: p = $\frac{m**b** - n**a**}{(m-n)}$. Special cases include the midpoint $\frac{**a**+**b**}{2}$ and the centroid $\frac{**a**+**b**+**c**}{3}$. The incenter uses side-length weights: $\frac{a**A**+b**B**+c**C**}{(a+b+c)}$ where a, b, c are opposite side lengths. Collinearity of three points A, B, C can be tested by verifying AB x AC = 0, or equivalently that there exist scalars summing to zero such that xa + yb + zc = 0. These formulas appear frequently in JEE, often combined with area calculations or property verification for triangles and quadrilaterals.