Let \(w = u - v\). Represent \(w\) on the diagram above.

Given that \(u = \left( \begin{array}{c}3\\2\\1\end{array} \right)\) and \(v = \left( \begin{array}{c}5\\n\\3\end{array} \right)\), where \(n \in \mathbb{Z}\), find \(n\).

METHOD 1

 A1A1      N2

Note: Award A1 for segment connecting endpoints and A1 for direction (must see arrow).

METHOD 2

 A1A1      N2

Notes: Award A1 for segment connecting endpoints and A1 for direction (must see arrow).

Additional lines not required.

[2 marks]

evidence of setting scalar product equal to zero (seen anywhere)     R1

eg   u \( \cdot \) v \( = 0,{\text{ }}15 + 2n + 3 = 0\)

correct expression for scalar product     (A1)

eg   \(3 \times 5 + 2 \times n + 1 \times 3,{\text{ }}2n + 18 = 0\)

attempt to solve equation     (M1)

eg   \(2n =  - 18\)

\(n =  - 9\)     A1     N3

[4 marks]