Coordinate systems can be attached to any point, but generally there is one or two points that are more convenient than others. For this problem, the coordiante system is placed at far right edge of the pipes. The position vector from the right edge of the pipe to joint B is

     r_B = r_Bxi + r_Byj + r_Bzk

         = 45i + 0j + 15k

The position vector of point Q (location of applied force F) can be determined when the wrench is rotated at an angle of α as

     r_Q = r_Qxi + r_Qyj + r_Qzk

         = 0i + 30 cosαj + (60 + 30 sinα)k

From vector addition, the position vector from joint B to point Q is

     r_B + r_BQ = r_Q

or
     r_BQ = r_Q - r_B

            = -45i + 30 cosαj + (45 + 30 sinα)k

Known Information

The system of two forces can be replaced by an equivalent system consisting of a force F_R and couple M_R applied at point O. The force F_R is found by summing the individual forces,

     F = F_xi + F_yj + F_zk

          = 0i - 80 sinαj + 80 cosαk

The moment of the force about joint B is given by

          M_B = r_BQ ×> F

The cross product in determinant form is

Expanding the equation gives

     M_B = (r_BQy F_z - r_BQz F_y)i + (r_BQz F_x - r_BQx F_z)j
                        + (r_BQx F_y - r_BQy F_x)k

Substituting the appropriate values and simplifing to determine the moment at joint B gives

     M_B = (2,400 + 3,600 sinα)i
                 + (3,600 cosα)j + (3,600 sinα)k

If the magnitude of M_B is plotted as a function of the angle α, then the moment is a maximum at α = 90°, with a value of 6,997 N-cm or about 70 N-m. This is approximately 62% greater than the moment at α = 0°.