1. ET-314 Week 11 Nov 7, 2014 Topic(s): 19.1 Vectors

2. Vectors

4. Practice Problems: x = 3 y = 6 r = __________  = __________ x = -2 y = 5 r = __________  = __________ r = 6  = 25  x = __________ y = __________ r = 5  = -65  x = __________ y = __________

5. Vector Additions In rectangular coordinates: V1 = (0.8, -0.7) V2 = (0.6, 1) V3 = V1 + V2 = ({0.8 + 0.6}, {-0.7 + 1}) = (1.4, 0.3)

6. Vector Additions In polar coordinates: V1 = (0.8  60  ) = (0.8 cos(60  ), 0.8 sin(60  )) = (0.4000, 0.6928) V2 = (0.7  -30  ) = (0.7 cos(-30  ), 0.7 sin(-30  )) = (0.6062,-0.3500) V3 = V1 + V2 = (1.0062, 0.3428) = (1.0062 2 + 0.3428 2 ) 0.5  tan -1 (0.34282 / 1.00622) = 1.0630  18.8141 

7. V1 + V2 Vector Subtractions In rectangular coordinates: V1 = (0.8, -0.7) V2 = (0.6, 1) V3 = V1  V2 = V1 + (-V2) = (0.8, -0.7) + (-0.6, -1) = ({0.8  0.6}, {-0.7  1}) = (0.1, -1.6) V1  V2

8. Practice Problems x = 2 y = 3 r =  =  x = 2 y = -5 r =  =  r = 20  = -128  x = y = r = 3  = 165  x = y =

9.  Practice Problems V1 = (0.8, 0.5), V2 = (0.7, -0.3), V3 = (0.6  50  ), V1 + V2 – V3 = ? More practice problems: