GCSE OCR Maths Vectors: Work out. a) \( \begin{pmatrix}

Work out. a) $ \begin{pmatrix} -3 \\ 2 \end{pmatrix} + \begin{pmatrix} 5 \\ 7 \end{pmatrix} $ b) $ \begin{pmatrix} 3 \\ 4 \end{pmatrix} -2 \begin{pmatrix} 1 \\ -3 \end{pmatrix} $ - OCR - GCSE Maths - Question 3 - 2018 - Paper 1

Question 3

$Work-out.-a)-$-\begin{pmatrix}--3-\\-2-\end{pmatrix}-+-\begin{pmatrix}-5-\\-7-\end{pmatrix}-$--b)-$-\begin{pmatrix}-3-\\-4-\end{pmatrix}--2--\begin{pmatrix}-1-\\--3-\end{pmatrix}-$-OCR-GCSE Maths-Question 3-2018-Paper 1.png$

Work out. a) $ \begin{pmatrix} -3 \\ 2 \end{pmatrix} + \begin{pmatrix} 5 \\ 7 \end{pmatrix} $ b) \( \begin{pmatrix} 3 \\ 4 \end{pmatrix} -2 \begin{pmatrix} 1 \\... show full transcript

Worked Solution & Example Answer:Work out. a) $ \begin{pmatrix} -3 \\ 2 \end{pmatrix} + \begin{pmatrix} 5 \\ 7 \end{pmatrix} $ b) $ \begin{pmatrix} 3 \\ 4 \end{pmatrix} -2 \begin{pmatrix} 1 \\ -3 \end{pmatrix} $ - OCR - GCSE Maths - Question 3 - 2018 - Paper 1

Step 1

(a)

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Answer

To compute the sum of the vectors, we add the corresponding components:

\begin{pmatrix} -3 \\ 2 \end{pmatrix} + \begin{pmatrix} 5 \\ 7 \end{pmatrix} = \begin{pmatrix}-3 + 5 \\ 2 + 7\end{pmatrix} = \begin{pmatrix}2 \\ 9\end{pmatrix}

Thus, the answer for part (a) is:

\begin{pmatrix} 2 \\ 9 \end{pmatrix}

Step 2

(b)

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Answer

For part (b), we first multiply the scalar by the vector:

2 \begin{pmatrix} 1 \\ -3 \end{pmatrix} = \begin{pmatrix} 2 \times 1 \\ 2 \times -3 \end{pmatrix} = \begin{pmatrix} 2 \\ -6 \end{pmatrix}

Then, we subtract this result from the first vector:

\begin{pmatrix} 3 \\ 4 \end{pmatrix} - \begin{pmatrix} 2 \\ -6 \end{pmatrix} = \begin{pmatrix} 3 - 2 \\ 4 - (-6) \end{pmatrix} = \begin{pmatrix} 1 \\ 10 \end{pmatrix}

Thus, the answer for part (b) is:

\begin{pmatrix} 1 \\ 10 \end{pmatrix}

Work out. a) \( \begin{pmatrix} -3 \\ 2 \end{pmatrix} + \begin{pmatrix} 5 \\ 7 \end{pmatrix} \) b) \( \begin{pmatrix} 3 \\ 4 \end{pmatrix} -2 \begin{pmatrix} 1 \\ -3 \end{pmatrix} \) - OCR - GCSE Maths - Question 3 - 2018 - Paper 1

Worked Solution & Example Answer:Work out. a) \( \begin{pmatrix} -3 \\ 2 \end{pmatrix} + \begin{pmatrix} 5 \\ 7 \end{pmatrix} \) b) \( \begin{pmatrix} 3 \\ 4 \end{pmatrix} -2 \begin{pmatrix} 1 \\ -3 \end{pmatrix} \) - OCR - GCSE Maths - Question 3 - 2018 - Paper 1

(a)

(b)

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