8 "on 3 A helium balloon is fixed by two tout ropes. Alice holds the m MWW u s. ' A ' PtlitiVi' to the balloon: Alice is 2 In Bash 3 In North and 1 m below the ala Elm rope Relative to the balloon Bob IS 3 In West, 1 In South and 3 m b the l y w the angle bowman the two ropes is '. oWhat is the value z? * ' ua al Question 4. Letv = bl , 2 Cl WE {fill-Hugh M m llyllliifl sfi &x uuuw au yuu: wuxxuug. UULLCbb auawclb XVJLIIOUU Justification "fill not receive IUII ITI'dIKbU QueStiOn 1 VVI'ite the number Z = 12 + 52' in polar form rem. Hence calculate 33. Give your answer in polar and rectangular form. (You can use a calculator for the trig.) 4 Marks . 1 -2 - ' QueSt10n2 LetXi=( Y=< 2 2 Z=(1 O). CalculateX3+Y3+Z3 3 2 Question 3. A helium balloon is fixed by two taut ropes. Alice holds the bottom end of one rope. Relative to the balloon, Alice is 2 in East, 3 in North and 1 m below the balloon. Bob holds the other rope. Relative to the balloon Bob is 3 In West, 1 rn South and z in below the balloon. At the balloon, the angle between the two ropes is UK What is the value of z? m up" al (12 QueStion 4 Let V = bi , W = bg E R3 be non-zero vectors. Let A be the point (a1, b1,C1) C1 Cg and B the point (ag, b2, Cg) and let 6 be the angle at the origin formed by line segments AC and OB. (a) Using the Law of Cosines in triangle AOB, show that ' , , - ; , '2 2 ,2 . "vu uwn casa - , (nvn + uwu - uv - wu ). / , that v . w ala? + blbg + am. This justifies the farm M m W tm