O-LevelAdditional MathematicsVectors in two dimensions4037/21 · May/June 2023 · Q610 Marks
The position vectors of the points P, Q and R relative to an origin O are (4/7), (8/5) and (x/y) respectively. The point R lies on PQ extended such that 3QR = 2PR. Use a vector method to find the values of x and y.
- (a)The position vectors of the points P, Q and R relative to an origin O are (4/7), (8/5) and (x/y) respectively. The point R lies on PQ extended such that 3QR = 2PR. Use a vector method to find the values of x and y.[3]
- (b)(i)You are given that i is a unit vector due east and j is a unit vector due north. Three vectors, a, b and c are in the same horizontal plane as i and j and are such that a+b = c. The magnitude and bearing of a are 5 and 210°. The magnitude and bearing of c are 10 and 330°. Find a and c in terms of i and j.[2]
- (b)(ii)Find the magnitude and bearing of b.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.
- [M1] 3(r - q) = 2(r - p) oe OR (x-8)/(y-5) = (x-4)/(y-7) oe
- [A1] x = 16 dep on vector method
- [A1] y = 1 dep on vector method
- [B1] a = -2.5i - (5√3/2)j isw
- [B1] c = -5i + 5√3j isw
- [B1] b = (-5 + 2.5)i + (5√3 + 2.5√3)j oe soi
- [M1] r = √((-2.5)² + (7.5√3)²)
- [A1] [r = ] 13.2 or 13.22875... rot to 4 or more sf
- [M1] tanα = (7.5√3)/2.5 oe or awrt 79.1 or tanβ = 2.5/(7.5√3) oe or awrt 10.9
- [A1] 349[.106...] rot to 3 or more sf
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →