(1) Cross product is NOT associative: a x (b x c) != (a x b) x c. Always evaluate the inner product first. (2) Cannot cancel in cross products: a x b = a x c does NOT imply b = c; it implies b - c is parallel to a. (3) Sign errors in determinant: Expand the 3x3 determinant carefully — the j component has a negative sign. (4) Dot product can be negative: cos(theta) < 0 when theta > 90 degrees. (5) Section formula ratio direction: The ratio m:n in the section formula is measured FROM the first point TO the second. Reversing the points reverses the ratio. (6) Unit vectors in bisector: Always normalize to unit vectors before adding/subtracting for angle bisectors.