Shape and Space 8
2 marks · HardABCD is a parallelogram. Given and , E is the point such that . Write the vector as a column vector.
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Must show: Correct calculation of as column vector
Also accept: 2 10
Common mistakes: Incorrect sign when subtracting vectors; Forgetting order: ED = OD - OE
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Marking points
M1 · 1 mark · Correct method for finding : uses or appropriate position vectors.
A1 · 1 mark · Accurately calculates and expresses the answer as . (follow-through)
Worked solution
Let’s find OE and OD using position vectors from O (the origin):
Similarly, . But we only need to find .
Wait: let's check the direction. We want = (OA + AD) - (OA + 2AB - AD) = AD - 2AB + AD = 2AD - 2AB. So the answer is correct.
So the final vector is .