Figure 1 Coordinate system

The law of sine and cosine. We are given a triangle with angles and sides as shown in Figure 2.38. Find unknown x-side.

In the Figure 2.39 shown a triangle. All sides are given. Find unknown angle.

Figure 2.40

Figure 2.41

Given two vectors with a magnitude of A = 11 m and B = 16 m and an angle between two vectors is 40⁰, Figure 2.40. Find the resultant vector.



Unit Vectors

42. 
    5 vectors are given as shown in Figure 2.41. The magnitudes of each vector are A = 5 m, B = 4 m, C = 7 m, D = 11 m, E = 8 m. Show each vector in terms of the unit vectors and .
    
43. 
    Find the x-, y- and, z- components of vector , draw diagrams for each case: (a) (b) ;.
    
44. 
    Suppose that . What is the magnitude of the vector?
    
45. 
    Given two vectors , . What is the magnitude of each vector? If we add these two vectors find the magnitude and direction of resultant vector.
    
46. 
    

    Figure 2.42

    Figure 2.43

    In Fig. 2.42 given two vectors. The vector A is 7 m and the vector B is 9 m. (a) Show vectors in terms of the unit vectors and . If we express vectors via the vector , where . (b) Find the magnitude and direction of .
    
47. 
    Given three vectors and , (a) What is the magnitude of vector ; (b) What is the magnitude .