Based on the figure, determine the magnitude of the resultant of OA , BC and DE .

Step-by-step solution

Let us resolve each vector into its x and y components. For vector OA : Magnitude = 2.0 m , angle with positive X-axis = 30^ OA = 2.0 (30^ ) i + 2.0 (30^ ) j OA = 2.0 ( 3 2 ) i + 2.0 ( 1 2 ) j = 3 i + 1.0 j For vector BC : Magnitude = 1.5 m , angle with negative X-axis = 60^ BC = -1.5 (60^ ) i + 1.5 (60^ ) j BC = -1.5 ( 1 2 ) i + 1.5 ( 3 2 ) j = -0.75 i + 0.75 3 j For vector DE : Magnitude = 1.0 m , directed along negative Y-axis DE = -1.0 j The resultant vector R is the sum of these three vectors: R = OA + BC + DE