11b makes no sense. If a vector is in the opposite direction to z it is parallel to z not perpendicular.
11c needs rewriting
12c ii) This cannot be proven. It is the definition of "parallel" for vectors.
12d) Best re-expressed in terms of points.
13 b Not true Consider v=(0,0,0) u=(1,2,3) and w=(4,5,6)
13 c is once again off syllabus. There are no matrices in the HSC courses and the question as it stands is almost incomprehensible. The trick to writing harder questions is to always make sure they are planted firmly in the centre of the course. They should be difficult because of depth, not due to the introduction of unfamiliar concepts.