Problems are shown below

Let v = (1, t) and w = (3, s) for some unknowns t, s. What is ? in order to make them parallel, v = ?w?

A cylinder has a central axis parallel to z-axis and through point (3, 2, 1) with radius 2. There is a basic plane z = 4 as well. Give an equation of the circle of intersection of the cylinder and the plane.

Find all points where the sphere x^2 + y^2 + z^2 = 1 and the line ?(t) = (0, 0, ? 1 3 ) + t(1, 1, 1) intersect, if any. If there is no such a point, write no points.

Problem 3 Let U = (Lt) and to = {3, s) for some unknowns Ls. 'What is A in order to make them parallel, v = Aw? Problem 4 A cylinder has a central axis parallel to z-axis and through point (3, 2, 1) with radius 2. There is a basic plane .2: = 4 as well. Give an equation of the circle of intersection of the cylinder and the plane. Problem 5 Find all points where the sphere 3:2 + y: + 2:2 = 1 and the line t] = (0,0, %) +t(1,1, 1] intersect, if any. If there is no such a point, write no points