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Vectors a and 4b are drawn on the grid - OCR - GCSE Maths - Question 20 - 2020 - Paper 3

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Question 20

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Vectors a and 4b are drawn on the grid. (a) Write vector a as a column vector. (b) Find vector b as a column vector.

Worked Solution & Example Answer:Vectors a and 4b are drawn on the grid - OCR - GCSE Maths - Question 20 - 2020 - Paper 3

Step 1

Write vector a as a column vector.

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Answer

To express vector a as a column vector, we first locate its coordinates on the grid. Assuming that vector a moves 3 units in the horizontal direction and 2 units in the vertical direction, we can represent it in column vector form as:

(32)\begin{pmatrix} 3 \\ 2 \end{pmatrix}

Step 2

Find vector b as a column vector.

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Answer

Next, we need to find vector b. Given that vector 4b is represented as a column vector that moves 6 units horizontally and 4 units vertically, we can derive vector b by dividing the coordinates of vector 4b by 4:

(6444)=(1.51)\begin{pmatrix} \frac{6}{4} \\ \frac{4}{4} \end{pmatrix} = \begin{pmatrix} 1.5 \\ 1 \end{pmatrix}

Thus, vector b can be expressed as:

(1.51)\begin{pmatrix} 1.5 \\ 1 \end{pmatrix}

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