A-LevelMathematicsVectors9709/12 · Feb/Mar 2017 · Q67 Marks
Relative to an origin O, the position vectors of the points A and B are given by OA = 2i + 3j + 5k and OB = 7i + 4j + 3k.
- (i)Use a scalar product to find angle OAB.[5]
- (ii)Find the area of triangle OAB.[2]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2017). The mark or mark type is shown in brackets.
- [B1] BA = OA - OB = -5i - j + 2k
- [M1] OA.BA = -10 - 3 + 10 = -3 soi by ±3
- [M1] |OA|x|BA| = sqrt(2^2 + 3^2 + 5^2) x sqrt(5^2 + 1^2 + 2^2)
- [M1] COS OAB = +/-3 / (sqrt(38) x sqrt(30))
- [A1] OAB = 95.1° (or 1.66°)
- [M1] Δ OAB = 1/2 sqrt(38) x sqrt(30) sin(95.1) Allow 1/2 sqrt(38) x sqrt(74) sin 39.4
- [A1] = 16.8 cao but NOT from sin 84.9 (1.482°)
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