with solution

1. Briefly answer the following questions. (a) How do you represent equations of functions in two variables in the Cartesian plane using a parameter? Is such a representation unique? (b) How do you determine the coordinate of a point in a parametric representation of a curve? (c) How do you get the domain of a function that is represented parametrically? (d) Can you sketch the graph of an equation in parametric form without removing the parameter? How? (e) How can you use either the dot or cross product in calculating area of regions enclosed by triangles and/or parallelograms? (f) How do you calculate the volume of a rectangular parallelepiped using vectors? 2. Find a Cartesian equation for the curve defined by the parametric equations: I = 2 - sect, y =3 - tan t. Sketch its graph. 3. Find a symmetric equation and a set of parametric equations of a line _ through the point (-5, 2, -1) and parallel to the line given by a = 5 - 2t,y = 2 +t,= = -8t. Sketch the line in R* space. 4. Find a general equation of the plane K containing the points (-1, 7, 4), (0, 2, -1), and (1, -1, 0). Sketch the plane in R* space. 5. Determine if the line given by x = 8-15t, y = 9t , = =5 + 18t and the plane given by 10r - 6y - 12z = 7 are parallel, orthogonal or neither