Final answer:
The torque's direction is determined by the right-hand rule and results in a torque vector for these vectors that points negatively along the z-axis. Using the cross product formula, the calculated torque is -1.05 N·m.
Step-by-step explanation:
To answer the questions requested by the student, we need to understand torque in a physics context. Torque, often represented by the Greek letter tau (T), is a measure of the turning force on an object. It is calculated as the cross product of the position vector (r) and the force vector (F), given by T = r x F.
A) To determine the direction of the torque using the right-hand rule, point your fingers in the direction of the position vector r, and then curl them in the direction of the force vector F. Your thumb will then point in the direction of the torque vector.
B) To calculate the torque, you take the cross product of r and F. In two dimensions with vectors given by components along the x and y axes, this simplifies to T = rxFy - ryFx. Substituting in the given values, T = (-0.450 m)(4.00 N) - (0.150 m)(-5.00 N) = -1.80 N·m + 0.75 N·m = -1.05 N·m. The negative sign indicates that the torque vector points in the negative direction of the axis perpendicular to the plane of r and F, which would be the z-axis in this case.