Question

Q4 / Given the points M (0.1, -0.2, -0.1), Ñ (-0.2, 0.1, 0.3), and Ž (0.4, 0, 0.1) in Cartesian coordinate.
Find: 1. The Vector RMN
2. The dot product Rmn. RMP
3. The angle between Rmn. RMP
4. Spherical coordinate for vector M

Answer 1

) M (0.1, -0.2,-0.1) N (-0.2,0.1,0.3) 2 (0.4, 0, 0.1) I Vecto - RMN 8 RMN =(-0.2,0.1,0.3) - (0.1, -0.2,-0.1) 3. RMN = (-0.3, 0.3, 0.4) २ dot Product RMN RMP :- RMP = (0.4,0,0.1) - (0.1,-0.2,-0.1) RMP =(0.3 (0.3, 0.2, 0.2,0.2)

RMN RMP = o (-0.3,0.3, 0.4). (0.3, 0.2,0.2) = -0.09 + 0.06 +0.08 = 0.05 : RMN • RMP = 0.05 between مل the RMN angle and RMP - Om = cost / RMN . RMP IRMNI IRMPI

& Om - cost 0.05 10.34 v0.17 RMN la 160.39 +(0.38 + (0.42 : IRMINI 0.34 lempl = 10.3+0,22 +0.22 IRMPI = 0.17 0 & OM 78° 14 Spherical Coordinate for vecto 44 M,

M (0.1, -0.2, -0.1) 크의 Vac² + y² + 22 e Jouya +(-0.272+(-0.192 DJ Jo.06 el = 0.245 → 0 = tant y tant (-0. -0.2 O.1 Q = -63.43

2.0 tan" (122 / x² + y² = tant Joo! 12+ (0.2) -0.1 tannl (- 2. 23) p . D] 65.9 :, Q Q = 180 65.90 of 114.09 N » Spherical co-ordinates, MC84,0,0) =M(0.245, -63.43, 114.09)