Mathematics · May / June 2022 · Paper 21 · Question 26
0580
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K A O L NOT TO SCALE B b a The diagram shows a triangle OAB and a parallelogram OALK. The position vector of A is a and the position vector of B is b. K is a point on AB so that . AK KB 1 2 | | = Find the position vector of L, in terms of a and b. Give your answer in its simplest form. [4]
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5 3 a + 1 3 b final answer [3]
4
M1 for 1 a + 1 2 2 − = − AK = 3 b or BK a b 3 3 3 ሬሬሬሬሬ⃗ oe soi
M1 for AL (or OK ) = a + their AK oe soi ሬሬሬሬሬ⃗ oe soi AL ) = b + their AK or OK (or BL = a + their AK
or M1 for a correct route e.g. OL , a + AL , b + BL
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