Final answer:
To find A+B and A-B, we find the components of forces A and B along the x and y axes. Analytically, we add/subtract the x-components and y-components separately. Geometrically, we place vector B at the head of vector A to find A+B, and at the head of -B to find A-B.
Step-by-step explanation:
To find A+B and A-B by both geometrical and analytical methods, we first need to find the components of forces A and B along the x and y axes. For A, with a magnitude of 6N and an angle of 36° with the positive x-axis, the x-component is given by Ax = A * cos(36°) and the y-component is Ay = A * sin(36°). Similarly, for B, with a magnitude of 7N and along the negative x-axis, the x-component is Bx = -B and the y-component is By = 0. Now, to find A+B, we add the x-components and y-components separately: (Ax + Bx) and (Ay + By). To find A-B, we subtract the x-components and y-components separately: (Ax - Bx) and (Ay - By).
Geometrically, we can represent forces A and B as vectors on a coordinate plane. The A vector is a 6N force at an angle of 36° with the positive x-axis, and the B vector is a 7N force along the negative x-axis. To find A+B, we place the tail of vector B at the head of vector A and draw a line connecting the tail of A to the head of B. This line represents the resultant force A+B. To find A-B, we place the tail of vector B at the head of vector A and draw a line connecting the tail of A to the head of -B. This line represents the resultant force A-B. The lengths of these lines can be measured to determine their magnitudes.