Evaluate:

Using vectors, find the area of the triangle ABC with vertices A (1, 2, 3), B (2, –1, 4) and C(4, 5, –1).

Evaluate:

Find the coordinate of the point where the line through (3, –4, –5) and (2, –3, 1) crosses the plane, passing through the points (2, 2, 1), (3, 0, 1) and (4, –1, 0).

Show that the differential equation (x e^y/x + y)dx = xdy is homogeneous. Find the particular solution of this differential equation, given that x = 1 when y = 1.