Vector a = \( \begin{pmatrix} 2 \\ 1 \end{pmatrix} \), vector b = \( \begin{pmatrix} -2 \\ -1 \end{pmatrix} \)\n\n(a) On each grid below, draw a vector to represent\n(i) 2a\n(ii) a + b\n\n(b) Emma says that if she draws vector a and vector b they will be the same.\nExplain why this is incorrect.\n\n(c) c = \( \begin{pmatrix} -12 \\ 0 \end{pmatrix} \)\nFind the value k so that k(a - b) = c. - OCR - GCSE Maths - Question 11 - 2017 - Paper 1

To find the vector ( a + b ), we first calculate:\n[ a + b = \begin{pmatrix} 2 \ 1 \end{pmatrix} + \begin{pmatrix} -2 \ -1 \end{pmatrix} = \begin{pmatrix} 0 \ 0 \end{pmatrix} ]\nOn the grid, start at the origin (0,0) and draw a vector that remains at the origin to represent ( a + b ).

Emma's statement is incorrect because the vectors a and b have different directions.\nThe vector a points to the right and up, while vector b points to the left and down.\nThus, they do not have the same direction or magnitude.

First, we calculate ( a - b ):\n[ a - b = \begin{pmatrix} 2 \ 1 \end{pmatrix} - \begin{pmatrix} -2 \ -1 \end{pmatrix} = \begin{pmatrix} 4 \ 2 \end{pmatrix} ]\nWe need to find k such that: [ k \begin{pmatrix} 4 \ 2 \end{pmatrix} = \begin{pmatrix} -12 \ 0 \end{pmatrix} ]\n\nFinding k:\nFrom the first component:\n[ 4k = -12 \Rightarrow k = -3 ]\nFrom the second component:\n[ 2k = 0 \Rightarrow k = 0 ]\nThus, k must equal -3.