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Question

Find the component form of the sum of u and v with direction angles u and v. Magnitude u = 14 Angle u = 45° Magnitude v = 70 Angle v = 180°

Answer

Now class, let's calculate the component form of the vector sum of u and v. We first need to express each vector in terms of its x and y components using trigonometric relationships. For u, we have x_u = 14cos45° = 9.89 and y_u = 14sin45° = 9.89. For v, we have x_v = 70cos180° = -70 and y_v = 70sin180° = 0. Adding the corresponding components of u and v, we get x_sum = -60.11 and y_sum = 9.89, giving us the answer, the vector quantity < -60.11, 9.89 >. Remember to convert the angle given in degrees to radians first!