Vector algebra problems in JEE typically fall into these categories: (1) Finding angles between vectors using cos(theta) = a.b/(|a||b|). (2) Determining parameter values for perpendicularity (a.b = 0) or parallelism (a x b = 0). (3) Area calculations using cross products — triangles, parallelograms, quadrilaterals. (4) Coplanarity/collinearity tests using scalar triple product or cross product. (5) Volume of parallelepiped or tetrahedron. (6) Section formula and centroid problems. (7) Problems using the constraint a + b + c = 0 with known magnitudes — square to find dot products. (8) Projection problems — scalar and vector projections. The most important strategy is recognizing which product to use: dot product for angles/projections/perpendicularity, cross product for areas/perpendicular vectors/parallelism, triple product for volumes/coplanarity. Always check if the problem has a shortcut via Lagrange's identity before computing full cross products.