The top mistakes in JEE vector algebra: (1) Assuming cross product is associative — a x (b x c) ≠ (a x b) x c in general. (2) Cancelling in cross products — a x b = a x c does NOT mean b = c; it means b - c is parallel to a. However, if BOTH a.b = a.c AND a x b = a x c, then b = c. (3) Sign error in determinant expansion — the j component carries a negative sign. (4) Confusing direction ratios with direction cosines — DCs satisfy $l^{2}$ + $m^{2}$ + $n^{2}$ = 1 while DRs don't. (5) Forgetting to normalize for angle bisector problems — must use unit vectors. (6) Misapplying section formula ratio — m:n is measured from the first point. (7) Assuming (a.b)c means "dot product is associative" — it's just scalar multiplication. Always verify intermediate steps.