Conceptual Understanding - simple

[elemis]

I would like to formally state that this is NOT a Homework question. I am NOT trying to cheat to get good marks. Instead the attached pdf file is a past examination question paper.

Just take my word for it and I can do without the aggro of mods jumping on back.

I would be EXTREMELY grateful if you could actually EXPLAIN the concept behind Question 6 B of the attached file.

The Examiner's Report that accompanies the question paper says this :

the first mark was for adding the two vectors together but many students then stated that this sum was equal to (i – 2j) rather than a multiple of it and were unable to make any progress.

I am more interested in the THEORY behind the part in bold. What is the concept ? Why do we equate the multiple of (i-2j) ?

 

[mathman]

Let c be the proportionality constant (between the parallel vectors).
4+p=c
-5+q=-2c
The left hand sides are the result of adding the given vectors. The right hand sides are for the given parallel.
Eliminate c from the two equations gives the stated result.

 

[elemis]

I see... Thank you very much.