Magnitude of A B units Direction of A B counterclockwise

(a)The vector sum is

C = A + B

The x and y components of vector C are

C_x = A_x + B_x = A * cos+ B * cos\'

and C_y = A_y + B_y = A *sin + B * sin\'

The vectors are

A = 9.10 units and B = 8.00 units

The angles are

= 52.5^o and \' = 180^o withthe positive x-axis

The magnitude of A + B is

|A + B| = [C_x² +C_y²]^1/2

The direction of A + B is

tan = (C_y/C_x)

or = tan^-1(C_y/C_x) =tan^-1(A * sin + B * sin\'/A * cos + B *cos\') counterclockwise from +x-axis

(b)The vector difference is

C = A - B

The x and y components of vector C are

C_x = A_x - B_x = A *cos - B * cos\'

and C_y = A_y - B_y = A *sin - B * sin\'

The vectors are

A = 9.10 units and B = 8.00 units

The angles are

= 52.5^o and \' = 180^o withthe positive x-axis

The magnitude of A - B is

|A - B| = [C_x² -C_y²]^1/2

The direction of A - B is

tan = (C_y/C_x)

or = tan^-1(C_y/C_x) =tan^-1(A * sin - B * sin\'/A *cos - B * cos\') counterclockwise from+x-axis