All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)
a and b are either zero vectors or parallel to each other.

(ii)
From (i)
$\hat{n}= \frac{1}{\sqrt{1+2^{2}+2^{2}}}\begin{pmatrix}1\\2\\-2\end{pmatrix}$

(iii)
$cos{\theta}=\frac{|\begin{pmatrix}1\\2\\-2\end{pmatrix}{\bullet}\begin{pmatrix}0\\0\\1\end{pmatrix}|}{\sqrt{9}}=\frac{2}{3}$

(i) tests students on understanding. Most students were able to deduce they are parallel. However, it did not cross their minds that the vectors could be zero vectors. They should take note that the question is worth 2 marks and it is far to generous for a simple answer.
Some students forgot and went ahead to evaluate the answer, disregarding that the question asks for COSINE of the acute angle so there is no need. Modulus is required since they are asking for an acute angle.

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