O-LevelAdditional MathematicsVectors in two dimensions4037/22 · May/June 2013 · Q46 Marks
The position vectors of the points A and B, relative to an origin O, are 4i – 21j and 22i – 30j respectively. The point C lies on AB such that AB = 3AC.
- (i)Find the position vector of C relative to O.[4]
- (ii)Find the unit vector in the direction OC.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2013). The mark or mark type is shown in brackets.
- [B1] (i) OC=OA+AC or OB-OA=3(OC-OA) soi or 3AC = 3(c₁ -4)i + 3(c₂ +21)j o.e. soi
- [B1] (i) ±(18i-9j) o.e. or OC = (2/3)OA + (1/3)OB
- [M1] (i) 4i-21j+(1/3)(their(18i-9j))o.e. or (1/3)(4i-21j)+(2/3)(22i – 30j) or 3(c1-4) = their 18 and 3(c2+21) = their (-9)
- [A1] (i) 10i-24j cao
- [M1] (ii) |OC| = √their10² + their(-24)² soi
- [A1 FT] (ii) (1/26)(10i-24j) isw (FT their xi + yj o.e.)
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