1. Find the equation of the line, and write the equation in the specified form. Be sure to define your parameter(s) if applicable

(a) the line parallel to m = (1, 3) and passes through the point (7, 4) (in vector form)

(b) the line that passes through the points (2, 5, 1) and (9, 3, 0) (in parametric form)

(c) the line that has a normal vector n = (2, 3) and passes through the point (5, 3) (in scalar form)

2. For the following two lines: `1 : (1, 4, 2) + t(2, 3, 5) and `2 : (1, 4, 2) + s(1, 2, 3),

(a) Determine the angle between L1 and L2, expressed to the nearest degree.

(b) Find, in parametric form, the equation of a line that is perpendicular to both L1 and L2, and passes through the point (3, 0, 0).

3. Find the equation of the plane, and write the equation in the specified form. Be sure to define your parameter(s) if applicable.

(a) the plane that has a normal vector n = (2, 3, 1) and passes through the point (5, 3, 7) (in scalar form)

(b) the plane that passes through the points (2, 3, 1), (1, 5, 4), and (3, 2, 0) (in scalar form)

(c) the plane parallel to the xy-plane and passing through the point (2, 3, 5) (in vector form)

4. Given the plane 3x y + z 12 = 0,

(a) Find any two points P and Q on the plane.

(b) Show that the vector PQ is perpendicular to the normal of the plane.

(c) Explain why part (b) is always true.

5. If possible, find the intersection of the following pair of lines in R^3 : L1 : (5, 2, 7)+s(3, 2, 6), s R and L2 : (0, 6, 3) + t(1, 5, 1), t R.

6. Find the scalar equation of the plane that passes through the point (3, 7, 1), and is perpendicular to the line of intersection of the planes 1 : x y 2z + 3 = 0 and 2 : 3x 2y + z + 5 = 0