calculus 4

Math 200 Quiz 2 Name: Section:

You must SHOW ALL WORK and USE CORRECT NOTATION to receive credit.

(1) Describe the surface whose equation is given as a sphere, a point, or one that has

no graph. If it is a sphere, give its center and radius. If it is a single point, give the

point.

(a) x2 + y2 + z2 + 2x−6y −4z + 5 = 0

(b) x2 + y2 + z2 −8x + 2y −4z + 21 = 0

(2) Give a vector ~w that has a length of 6 and the same direction as ~v = 〈0, 5, 4〉

1

(3) Find the acute angle formed by two diagonals of a unit cube.

(4) Let ~v = 3~i +~j −2~k and ~b = 2~i−~k. Express ~v as the sum of a vector parallel to ~b and a vector orthogonal to ~b. Clearly label which part of your answer is parallel to

~b and which part is orthogonal to ~b.

2