Final answer:
To determine the magnitude and direction of the sum of two vectors, decompose each vector into x and y components, add these components to get the resultant's components, then use these to calculate the resultant vector's magnitude and direction.
Step-by-step explanation:
To find the magnitude and direction of the vector A+B, we can use analytical methods to decompose each vector into its x and y components, then add the components of the two vectors separately, and finally calculate the resultant vector's magnitude and direction.
For vector A: The x-component is given by Ax = A cos θ, and the y-component by Ay = A sin θ. Because vector A is below the positive x-axis, its y-component will be negative.
For vector B: Its y-component is By = B cos θ and the x-component is Bx = B sin θ. Because it's left of the positive y-axis, its x-component will be negative.
Once we have the components, we add the x-components of both vectors to find the resultant's x-component, and similarly for the y-component. The magnitude of the resultant vector R is found using the Pythagorean theorem, R = √(Rx2 + Ry2). The direction θR of vector R is found using the arctan function, θR = atan(Ry/Rx).