Building blocks

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Problem

Here are some vectors:

• $\mathbf{a}=\begin{pmatrix}6\\1\end{pmatrix}$
• $\mathbf{b}$ has magnitude $2\sqrt{2}$ and direction $45^\circ$ anti-clockwise from the $x$-axis

• $\mathbf{c}$ has magnitude $4$ in the positive $x$ direction

• $\mathbf{d}=3\mathbf{i}-\mathbf{j}$

• $\mathbf{e}=7\mathbf{i}-3\mathbf{j}$

• $\mathbf{f}$ is $2$ units in the negative $x$ direction and $3$ units in the positive $y$ direction
• $\mathbf{g}=\begin{pmatrix}-2\\4\end{pmatrix}$

Select a starting point, $M(2,5)$ or $N(3,1)$, and two of the vectors from the list so that the sum of the vectors will get you from your start to the target, $T(7,6)$.

How many different ways can you pair up vectors from the list to get to the target?

Can you add three of the vectors to get from one of the starts to the target?