Using vector methods, prove that the angle subtended by a diameter of a circle at any point on the circumference is a right angle.

Find the work done by a constant force $\vec{F} = 3\hat{i} - 2\hat{j} + 4\hat{k}$ acting on a particle that moves from point $A(1, 2, -1)$ to point $B(3, -1, 2)$.