The vectors a = (7, 2), b = (m, −3) and c = (−5, 3) are such that a + 2b = c. Find the values of m and n.

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Here is the solution for question (3) from the image.

3) Given $\vec{PQ} = \begin{pmatrix} 2 \\ 3 \end{pmatrix}$ and $\vec{OQ} = \begin{pmatrix} -1 \\ 4 \end{pmatrix}$ . Find the coordinates of P.

Use the relationship between displacement and position vectors.
The displacement vector $\vec{PQ}$ is found by subtracting the position vector of the starting point P ( $\vec{OP}$ ) from the position vector of the ending point Q ( $\vec{OQ}$ ).
$\vec{PQ} = \vec{OQ} - \vec{OP}$
To find the coordinates of P, we need to solve for $\vec{OP}$ . Rearrange the equation:
$\vec{OP} = \vec{OQ} - \vec{PQ}$
Substitute the given vectors into the rearranged equation.
$\vec{OP} = \begin{pmatrix} -1 \\ 4 \end{pmatrix} - \begin{pmatrix} 2 \\ 3 \end{pmatrix}$
Perform the vector subtraction.
Subtract the corresponding components:
$\vec{OP} = \begin{pmatrix} -1 - 2 \\ 4 - 3 \end{pmatrix}$
Calculate the resulting components.
$\vec{OP} = \begin{pmatrix} -3 \\ 1 \end{pmatrix}$
State the coordinates of P.
The position vector $\vec{OP} = \begin{pmatrix} -3 \\ 1 \end{pmatrix}$ means that the coordinates of point P are $\boxed{(-3, 1)}$ .

The vectors a = (7, 2), b = (m, -3) and c = (-5, 3) are such that a + 2b = c. Find the values of m and n.