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 = (mb + na)/(m+n). For external division: p = (mb - na)/(m-n). Special cases include the midpoint (a+b)/2 and the centroid (a+b+c)/3. The incenter uses side-length weights: (aA+bB+cC)/(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.