Question

1. find the components of each vector that is presented in the Cartesian plane and find the resulting vector in vector form

2. using the data from the previous exercise, find the magnitude and direction of the resulting vector

1. Halle los componentes de cada vector que se presenta en el plano cartesiano y halle el vector resultante en forma vectorial. 20 puntos Componentes Vector A: (muestre el proceso completo) B = 25 N C Componentes Vector B: (muestre el proceso completo) 607 C = 20N Componentes Vector C: (muestre el proceso completo)

Answer 1

* If à is any vector making on angle o with positive x-direction, then it's i and yo.components are given by : _Ax = A cos@ and Ay = A sino where A is magnitude of vector Ā. 1 Components vector À of Ā _Axe - A coso Ay Asino = 30 cos 30º = = 30 sin 30° - 26 N 15 N - Ø Components of vector Š O: angle made by vector B with ta-axis! is _ = 180° - 20° = 160° Bx = B Coso = 25c0s 160º = By = B sino - 25 sin 160°= -23.5 N 8.55 N & © Components of vector ē Anule made by vectoo T with + x - axis is 0 = 180° + 60° - 240° i Ca - Ccoso = 20 cos 2400 = -ION Cy - Csino = 20 sio 240° = -17.30

Resultant : Resultant of Ā B & Ĉ e is given by Ř = (Axt. Bx + (x) i + (Ay + By + Cy); - ( 26 - 23.5 -10) î + (15 +8.55 – 17.3) î Ř = -7.5 î + 6.25 î Magnitude of Resultant : 1 TRI = V Rat + Rý = V(-7.5)2 + (6-25)2 1-7.52 :. Magnitude IRL = 9.76 N. Direction of Resultant : o too celotne tant ( -5,25 ) - - 39.8° .: Direction © = 39.8° above -ve x-axis or 0 - 140.2° above +x-axis il