Vector A is 3.0 units in length and points along the positivex-axis: vector B is

Question

Vector A is 3.0 units in length and points along the positivex-axis: vector B is 4.0 units in length and points along adirection 150 degrees from the positive x-axis. What is themagnitude of the resultant when vectors A and B are added? I need to know the steps. Vector A is 3.0 units in length and points along the positivex-axis: vector B is 4.0 units in length and points along adirection 150 degrees from the positive x-axis. What is themagnitude of the resultant when vectors A and B are added? I need to know the steps.

Explanation / Answer

. 1.   I shall use bold face type to denotevectors. 2.   I shall use "âx"and "ây" to denote the unitvectors in the x-direction and y-direction, respectively. . 3.   A = 3âx 4.   B = (4)*cos(150degrees) âx + (4)*sin(150degrees) ây = (-3.46)âx + (2.00)ây 5.   C = A +B = [(3) + (-3.46)]âx +[2.00]ây =(-0.46)âx +(2.00)ây 6.   |C| = { (-0.46)2 +(2.00)2 }(1/2) = 2.052 7.   = arctan[(2.0)/(-0.46)] = -77.05degrees = 102.95 degrees .

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