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Vector a = \( \begin{pmatrix} 3 \\ 2 \end{pmatrix} \) and vector b = \( \begin{pmatrix} -1 \\ -4 \end{pmatrix} \) - OCR - GCSE Maths - Question 17 - 2023 - Paper 2
Question 17
Vector a = \( \begin{pmatrix} 3 \\ 2 \end{pmatrix} \) and vector b = \( \begin{pmatrix} -1 \\ -4 \end{pmatrix} \). (a) On the grid, draw vector a. (b) On the grid,... show full transcript
Worked Solution & Example Answer:Vector a = \( \begin{pmatrix} 3 \\ 2 \end{pmatrix} \) and vector b = \( \begin{pmatrix} -1 \\ -4 \end{pmatrix} \) - OCR - GCSE Maths - Question 17 - 2023 - Paper 2
Step 1
(a) On the grid, draw vector a.
Answer
To draw vector a, start at the origin (0, 0) on the grid. Move 3 units to the right (positive x-direction) and 2 units up (positive y-direction). Mark the endpoint of the vector at the point (3, 2). Draw an arrow from the origin to this point to represent vector a.
Step 2
(b) On the grid, draw vector a + b.
Answer
First, calculate vector a + b:
[ a + b = \begin{pmatrix} 3 \ 2 \end{pmatrix} + \begin{pmatrix} -1 \ -4 \end{pmatrix} = \begin{pmatrix} 3 - 1 \ 2 - 4 \end{pmatrix} = \begin{pmatrix} 2 \ -2 \end{pmatrix} ]
To draw vector a + b, start at the origin (0, 0). Move 2 units to the right and 2 units down. Mark the endpoint of vector a + b at the point (2, -2) and draw an arrow from the origin (0, 0) to (2, -2).