Tutorial 1

Tutorial 1 - ρ = 2 a sin ϕ . 4. If a and b are unit...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
MATH1211/10-11(1))/Tu1 THE UNIVERSITY OF HONG KONG DEPARTMENT OF MATHEMATICS MATH1211 Multivariable Calculus 2010-11 1st Semester: Tutorial 1 Date of tutorial classes: September 13–17. 1. Give a set of parametric equations for the plane determined by the equation 2 x - 3 y +5 z = 30. 2. Let a and b be vectors in R n . Show that if k a - b k > k a + b k , then the angle between a and b is obtuse (i.e., greater than π/ 2.) 3. (a) Graph the curve in R 2 having polar equation r = 2 a sin θ , where a is a positive constant. (b) Graph the surface in R 3 having spherical equation
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ρ = 2 a sin ϕ . 4. If a and b are unit vectors in R 3 , show that k a × b k 2 + ( a · b ) 2 = 1 . 5. Show that the two lines ‘ 1 : x = t-3 , y = 1-2 t, z = 2 t + 5 ‘ 2 : x = 4-2 t, y = 4 t + 3 , z = 6-4 t are parallel, and find an equation for the plane that contains them. 6. Sketch and describe the surfaces in R 3 determined by the following equations. (a) 2 x 2 + 2 y 2 + z 2 = 1 (b) x 2-y 2 + z 2 = 1 (c) x 2-y 2-z 2 = 1 (d) x 2-y 2 + z 2 = 0 1...
View Full Document

This note was uploaded on 05/04/2011 for the course MATH 1211 taught by Professor Wang during the Spring '11 term at HKU.

Ask a homework question - tutors are online