Consider the vectors?

Consider the vectors, u =(2, – 4), v = (4, 2), and w = v – u.





(a) Find the magnitude, and the direction of the vectors, u, v, and w.














(b) Find the area, A, of the triangle, T, the three sides of which are made by the vectors, u, v and w. What kind of triangle is T?














(c) Find the volume of the prism the length of which is, l = 6, and the cross-section of which is the triangle made by the vectors, u and v.

Consider the vectors?
(a) vector u has a magnitude of Sqrt(4+16) = Sqrt(20) and a direction of arctan(-4/2) = -63.435 degrees. vector v has a magnitude of Sqrt(16+4) = Sqrt(20) and a direction of arctan(2/4) = 26.565 degrees. vector w has a magnitude of Sqrt(4+36) = Sqrt(40) and a direction of arctan(6/2) = 71.565 degrees.





(b) The triangle has an area = (1/2)(Sqrt(20))(Sqrt(20)) = (1/2)(20) = 10 square units. It is a right triangle because the vectors v and -u are perpendicular to each other (the product of their slopes is -1).





(c) The volume of a prism would simply be the area of the base, 10 units from above, times a length of 6. So the answer is 60 cubic units.
Reply:Whenever I come across a question on yahoo answers that starts with "consider the 2 vectors".. I ussually start to panic and run away as fast as possible, even if I dont have any clothes on.