The vector a and the vector b are shown on the grid - Edexcel - GCSE Maths - Question 11 - 2018 - Paper 2

To find a + 2b, we first need to determine the coordinates of vector b. Let's say vector b has a tail at point O(0, 0) and head at (6, 2). Then, vector b can be represented as:

$\textbf{b} = \begin{pmatrix} 6 \\ 2 \end{pmatrix}$

Next, calculate 2b:

1. Multiply vector b by 2: $2\textbf{b} = 2 \begin{pmatrix} 6 \\ 2 \end{pmatrix} = \begin{pmatrix} 12 \\ 4 \end{pmatrix}$

Now, we can find a + 2b:

$\textbf{a} + 2\textbf{b} = \begin{pmatrix} 4 \\ 4 \end{pmatrix} + \begin{pmatrix} 12 \\ 4 \end{pmatrix} = \begin{pmatrix} 4 + 12 \\ 4 + 4 \end{pmatrix} = \begin{pmatrix} 16 \\ 8 \end{pmatrix}$

Thus, the final result for a + 2b as a column vector is:

$\textbf{a} + 2\textbf{b} = \begin{pmatrix} 16 \\ 8 \end{pmatrix}$