Two vectors, a and b, are shown on the 1 centimetre grid below - OCR - GCSE Maths - Question 10 - 2018 - Paper 1
Question 10
Two vectors, a and b, are shown on the 1 centimetre grid below.
Show that the vector a + 2b has length 7 cm.
You may use the grid below.
Worked Solution & Example Answer:Two vectors, a and b, are shown on the 1 centimetre grid below - OCR - GCSE Maths - Question 10 - 2018 - Paper 1
Step 1
Draw vector 2b on grid
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Answer
To find the vector 2b, first identify the coordinates of vector b from the grid. If vector b is represented by the coordinates (x, y), then the vector 2b will be represented by (2x, 2y). Draw this vector on the grid, ensuring it is correctly labelled.
Step 2
Draw vector a on grid
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Answer
Identify the coordinates of vector a from the grid. These coordinates will remain the same when drawing vector a. Draw vector a on the grid, correctly labelled.
Step 3
Combine vectors a and 2b
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Answer
To find vector a + 2b, start from the tip of vector a and draw the vector 2b from this point. This will create a new vector which connects the starting point of vector a to the tip of vector 2b.
Step 4
Measure the length of vector a + 2b
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Answer
Use a ruler to measure the length of the resultant vector a + 2b on the grid. Ensure that the measurement is consistent with the given scale of the grid. The expected length is 7 cm, which should be indicated clearly on the diagram.
