Typos in practice problems of MA1201 This file provides a (not necessarily complete) list of typos in practice problem set of MA1201. 1 Chapter 4 (vector algebra) Q1(e ii) ~ b = − 5 ̂ BC = − 5 − − → BC |− − → BC | = − 10 √ 22 ~ i + 15 √ 22 ~ j + 15 √ 22 ~ k Q2(b) − − → AX = − − → OX − − → OA . Thus − − → OX = − − → AX + − → OA = ( 2 3 ~ i + 2 3 ~ j + 2 3 ~ k ) + ( ~ j − ~ k ) = 2 3 ~ i + 5 3 ~ j − 1 3 ~ k Q6(a) The vector − − → BA = − → OA − − − → OB = 3 ~ i + ~ j . Thus cos θ = − − → BA · − − → BC |− − → BA | · |− − → BC | = 3(1) + 1(2) √ 3 2 + 1 2 √ 1 2 + 2 2 = 5 √ 10 √ 5 = 1 √ 2 So θ = π 4 Q8(a) cos θ = 1 2 . So, θ = π 3 = 60 ◦ Q12(d) ~ a × ~ b = 3 ~ i + 3 ~ j − 3 ~ k 2 Chapter 1 (Basic concept in integration) Q3 (b) ∫ 1 − 1 cos(3 x + 1) dx = 1 3 sin(3 x + 1) | 1 − 1 = 1 3 (sin 4 − sin( − 2)) = 1 3 (sin 4 + sin 2).