Update (16/02/20)What a mess. Thanks to Damo for pointing out the problem, and thanks to the commenters for figuring out the nonsense.
In general form, the (intended) scenario of the exam question is
The vector resolute of in the direction of is ,which can be pictured as follows: For the exam question, we have , and .
Of course, given and it is standard to find . After a bit of trig and unit vectors, we have (in must useful form)
The exam question, however, is different: the question is, given and , how to find .
The problem with that is, unless the vectors and are appropriately related, the scenario simply cannot occur, meaning cannot exist. Most obviously, the length of must be no greater than the length of . This requirement is clear from the triangle pictured, and can also be proved algebraically (with the dot product formula or the Cauchy-Schwarz inequality).
This implies, of course, that the exam question is ridiculous: for the vectors in the exam we have , and that’s the end of that. In fact, the situation is more delicate; given the pictured vectors form a right-angled triangle, we require that be perpendicular to . Which implies, once again, that the exam question is ridiculous.
Next, suppose we lucked out and began with perpendicular to . (Of course it is very easy to check whether we’ve lucked out.) How, then, do we find ? The answer is, as is made clear by the picture, “Well, duh”. The possible vectors are simply the (non-zero) scalar multiples of , and we’re done. Which shows that the mess in the intended solution, Answer A, is ridiculous.
There is a final question, however: the exam question is clearly ridiculous, but is the question also stuffed? The equations in answer A come from the equation for above and working backwards. And, these equations correctly return no solutions. Moreover, if the relationship between and had been such that there were solutions, then the A equations would have found them. So, completely ridiculous but still ok?
The question is framed from start to end around definite, existing objects: we have THE vector resolute, resulting in THE values of m, n and p. If the VCAA had worded the question to find possible values, on the basis of a possible direction for the resolution, then, at least technically, the question would be consistent, with A a valid answer. Still an utterly ridiculous question, but consistent. But the VCAA didn’t do that and so the question isn’t that. The question is stuffed.