1) Let In be the line through the points (1, 0, -1) and (-1, 1, 0), and let L2 be the line through the points (3, 1, -1) and (4, 5, -2). Show that I and Ly are skew, and then find the distance between the two lines. 2) Let u and of be any two non-zero vectors in R. We have already defined the projection of + onto i, with the formula projavi = 1 - For any given plane II, we can also define the projection of + onto the plane II by projov = v - projay where n is any vector normal to II So, if II is the plane with equation ar + by + oz = d and v = (v1, v2, v3), find a formula (involving just a, b, c, v1, v2, v3) for the projection of the vector of onto the plane II Note: Your formula should tell me how to explicitly compute each component of the projection from the values a, b, c, v1, 12, 13 3) Find the unit tangent vector T' and unit normal vector N for the param- eterized curve r(t) = (t - sint, 1 - cost, 21). 4) An object is moving through Re in such a fashion that at any time t the acceleration of the object is a = (1, t, +2 ) At time t = 0 the velocity of the object is (3, 2, 1) and its position is at the origin. Find the equation of the osculating plane to the curve at time t = 2, and find the curvature of the object's path at t = 2