1. Vector A points due west and vector B points due south. a) In what direction
ID: 1686409 • Letter: 1
Question
1. Vector A points due west and vector B points due south.a) In what direction does A - B point?
2. Vector A has a magnitude of 38 units and points west Vector B has a magnitude of 38 units and points south.
a)What is the algebraic expression that gives the magnitude of A-B ? Express your answer in terms of the magnitude A of vector A and the magnitude B of vector B . (Use A for Vector A and B for Vector B).
b)What is the actual magnitude of A-B?
c) What is the algebraic expression that gives the angle ? that specifies the direction of A - B with respect to due west? Express your answer in terms of an inverse trigonometric function (e.g., atan) and the magnitude A of vector A and the magnitude B of vector B. Theta =
Explanation / Answer
1. Vector A points due west vector B points due south So,opposite to vector B is in north direction Therefore direction of A - B point in north west direction 2. Vector A has a magnitude A = 38 units it points along west So, vector A = -38 i Vector B has a magnitude B = 38 units and it points south So, vector V = -38 j where i , j are the unit vectors along east and north directions a)the algebraic expression of the magnitude of A-B = sqrt [ A^ 2+ B^ 2 -2AB cos 90 ] = sqrt[ A^ 2+ B^ 2 ] since cos 90 = 0 Since angle between vector A and B = 90 degrees b)the actual magnitude of A-B= sqrt [ 38^ 2 + 38 ^ 2 ]= 53.74 units c) the algebraic expression that gives the angle theta = tan-1[ B sin 90 / (A+B cos 90 )] = tan-1( B / A )
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