Question

Question

If $\underset{U}{\rightarrow}=<1,1,2>, and \underset{V}{\rightarrow}=<0,2,1>$

a) Find the angle between $\underset{U}{\rightarrow}and\underset{V}{\rightarrow}$

b) Find a scalar projection and a vector projection of $\underset{V}{\rightarrow}onto\underset{U}{\rightarrow}$

Answer 1

(a): Concept used! Angle between two vector a and to is co, then eos ( If a 121= la 1151 Laxe, ay, az7 (x²+ (ays? + (92) 2 u 3- 21.1.2 20,2, 13 bet V is. a, then angle between to and uv Coso 17111 00800= 11,2). <0.2.1 7 <ulas II < 0,9,131 (1.0) + (1.2) + (2.1) 02 403 4(0) 21602+(3724 02 4 16.15 4 130 Cosco

va (b) Scalar component of rector a on b lal cosce where a: angle between a and be (al cosce vector boogection = (al coscel b ) 5 unit vector in direction of . Izooloo 7 <0,2,12 = 21,1,27 Scalas projection of y onto o = 171 cosco - K 0,2.15ly ? 4 JBO'T Colc = from ca) om

Veget co* 4use X • - - 15 16 2 JG 256 Vector projection = vectos poojection (Scalao booguation) ( Scal ) 9 <1,1,2) ) 2J6 K1, 2, 271 < 11.27 I 20² + 1² + (212 FACTORS. <1,2%