d $4 \mathrm{~cm}$ relation. 4
7.a) Given that $m=2 i-5 j$ and $n=-7 i+17 j$, calculate $|m+n|$
b. If $p=\left(\begin{array}{c}2 \\ -1\end{array}\right), q=\left(\begin{array}{l}1 \\ 3\end{array}\right)$, and $r=\left(\begin{array}{c}5 \\ -6\end{array}\right)$, calculate:
i) $|u|$ if $u=3 q+r$
ii) the bearing of $u$
iii) $m$ and $n$ such that $r=m p+n q$ where $m$ and $\boldsymbol{n}$ are scalars.

Step 1 ：Given vectors m and n as m = 2i - 5j and n = -7i + 17j respectively.

Step 2 ：The sum of vectors m and n can be calculated by adding the corresponding components of the vectors. So, m + n = (2 - 7)i + (-5 + 17)j = -5i + 12j.

Step 3 ：The magnitude of a vector is calculated using the Pythagorean theorem, which states that the magnitude of a vector is the square root of the sum of the squares of its components.

Step 4 ：Applying the Pythagorean theorem to the sum of vectors m and n, we get |m + n| = \(\sqrt{(-5)^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169}\)

Step 5 ：Calculating the square root of 169 gives us 13.0.

Step 6 ：\(\boxed{13.0}\) is the magnitude of the sum of vectors m and n.