1. SMN 3033 Multivariate Calculus
Semester 1 Session 2011/2012
Exercise 1: Geometry of Space
1. Describe the surface whose equation is given by x2 + y 2 + z 2 8y = 0:
2. Show that (4; 6; 12) ; (2; 7; 6) ; and ( 2; 5; 7) are vertices of a right triangle.
3. Find the equation of the sphere whose center is ( 4; 0; 6) and passes through (2; 2; 3) :
4. Sketch the surface whose equation is given by x2 + y 2 = 9:
5. Name the surface with equation: z = 4x2 + y 2 :
6. Name the surface given by the equation: x2 + y 2 z2 2x + 4y 2z = 0:
7. Convert:
3 2
(a) 3; ; from spherical coordinates to rectangular coordinates.
4 3
p p
(b) 3; 1; 2 3 from rectangular coordinates to spherical coordinates.
p p
(c) 3; 1; 2 3 from rectangular coordinates to cylindrical coordinates.
2
(d) 3; ; from spherical coordinates to cylindrical coordinates.
6 3
1