Maria starts at the origin and walks along all of the vector $2 extbf{i} + 3 extbf{j}$, then walks along all of the vector $3 extbf{i} - 2 extbf{j}$ and finally along all of the vector $4 extbf{i} - 3 extbf{j}$ - HSC - SSCE Mathematics Extension 1 - Question 4 - 2020 - Paper 1

First Vector: Maria walks along the vector $2 extbf{i} + 3 extbf{j}$.\n
Displacement: $D_1 = \begin{pmatrix} 2 \\ 3 \end{pmatrix}$.\n\n2. Second Vector: Next, she walks along the vector $3 extbf{i} - 2 extbf{j}$. \n
Displacement: $D_2 = \begin{pmatrix} 3 \\ -2 \end{pmatrix}$. \n

Total Displacement after two vectors: $D_{total1} = D_1 + D_2 = \begin{pmatrix} 2 + 3 \\ 3 - 2 \end{pmatrix} = \begin{pmatrix} 5 \\ 1 \end{pmatrix}$. \n\n3. Third Vector: Finally, she walks along the vector $4 extbf{i} - 3 extbf{j}$. \n
Displacement: $D_3 = \begin{pmatrix} 4 \\ -3 \end{pmatrix}$. \n

Total Displacement: $D_{total2} = D_{total1} + D_3 = \begin{pmatrix} 5 + 4 \\ 1 - 3 \end{pmatrix} = \begin{pmatrix} 9 \\ -2 \end{pmatrix}$.