12 (a)
PQ =
\left( \frac{3}{4} \right)
Work out 5PQ - OCR - GCSE Maths - Question 12 - 2018 - Paper 1
Question 12
12 (a)
PQ =
\left( \frac{3}{4} \right)
Work out 5PQ.
(b) Find the values of h and k.
\left( \frac{h}{5} \right) + \left( \frac{2}{|k|} \right) \left( ... show full transcript
Worked Solution & Example Answer:12 (a)
PQ =
\left( \frac{3}{4} \right)
Work out 5PQ - OCR - GCSE Maths - Question 12 - 2018 - Paper 1
Step 1
Find 5PQ
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Answer
To find the vector 5PQ, we start with PQ represented as ( \left( \frac{3}{4} \right) ). Therefore:
5PQ=5×(43)=(415)
Step 2
Find the values of h and k
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Answer
We have the equation:
(5h)+(∣k∣2)(33)=(0)
From the equation, we know that:
( \frac{h}{5} + \frac{2}{|k|} = 0 )
This leads us to ( |k| ) needing to be 2 (from second part of the question, thus ( k = 2 ) or ( k = -2 ))
Substituting for k in the first equation, we derive that ( h = -2 )
Thus, the values are:
( h = -2 )
( k = 2 )
Step 3
Use the diagram to complete this vector sum
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Answer
From the diagram, we conclude:
AB+BC+CA=(0−8)+(08)+(0−8)=(00)
Step 4
Give a reason why the answer could be written down without working
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Answer
The answer could be written down without working because the vector sum forms a closed loop returning to the starting point. Hence, the resultant vector is effectively zero.
