# hw243 - MA 243 Calculus III - Spring 2011 Assignments...

This preview shows pages 1–5. Sign up to view the full content.

MA 243 Calculus III - Spring 2011 Jacobs Assignments Assignment 1. Spheres and Other Surfaces Read 13.1 - 13.2 and 13.6 You should be able to do the following problems: Section 13.1/Problems 11 - 18, 20 - 22 Section 13.6/Problems 1 - 48 Hand in the following problems: 1. The equation x 2 + y 2 + z 2 =2 z - 4 y + 4 describes a sphere. Find the center and the radius of this sphere? 2. A particular sphere with center ( - 3 , 2 , 2) is tangent to both the xy -plane and the xz -plane. It intersects the xy -plane at the point ( - 3 , 2 , 0). Find the equation of this sphere. 3. Suppose (0 , 0 , 0) and (0 , 0 , - 4) are the endpoints of the diameter of a sphere. Find the equation of this sphere. 4. Find the equation of the sphere centered around (0 , 0 , 4) if the sphere passes through the origin. 5. Describe the graph of the given equation in geometric terms, using plain, clear language: z = ± 1 - x 2 - y 2 Sketch each of the following surfaces 6 . z = - ± x 2 + y 2 7 . z =1 - y 2 8 . z =4 - x - y 9 . z - x 2 - y 2 10 . x 2 + z 2 = 16

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Assignment 2. Dot and Cross Products Read 13.3 and 13.4 You should be able to do the following problems: Section 13.3/Problems 1 - 28 Section 13.4/Problems 1 - 32 Hand in the following problems: 1. Let ) u = ± 0 , 1 2 , 3 2 ² and ) v = ± 2 , 3 2 , 1 2 ² a) Find the dot product b) Find the cross product 2. Let ) u = ) j + ) k and ) v = ) i + 2 ) j . a) Calculate the length of the projection of ) v in the ) u direction. b) Calculate the cosine of the angle between ) u and ) v 3. Consider the parallelogram with the following vertices: (0 , 0 , 0) (0 , 1 , 1) (1 , 0 , 2) (1 , 1 , 3) a) Find a vector perpendicular to this parallelogram. b) Use vector methods to ±nd the area of this parallelogram. 4. Use the dot product to ±nd the angle between the diagonal of a cube and one of its faces 5. Let L be the line that passes through the points (0 , 1 , 6) and (0 , 3 , 2). Find the length of the projection of ) k = ± 0 , 0 , 1 ² on the line L .
Assignment 3. Lines and Planes Read 13.5 You should be able to do the following problems: Section 13.5/Problems 1 - 58 Hand in the following problems: 1a. Find the equation of the line that passes through (0 , 0 , 1) and (1 , 0 , 2). b. Find the equation of the plane that passes through (1 , 0 , 0) and is perpendicular to the line in part (a). 2. The following equation describes a straight line: ) r ( t )= ± 1 , 1 , 0 ² + t ± 0 , 2 , 1 ² a. Find the angle between the given line and the vector ) u = ± 1 , - 1 , 2 ² . b. Find the equation of the plane that passes through the point (0 , 0 , 4) and is perpendicular to the given line. 3. The following two lines intersect at the point (1 , 4 , 4) ) r = ± 1 , 4 , 4 ² + t ± 0 , 1 , 0 ² ) r = ± 1 , 4 , 4 ² + t ± 3 , 5 , 4 ² a. Find the angle between the two lines. b. Find the equation of the plane that contains every point on both lines. 4. The following equation describes a straight line: ± x, y, z ² = ±- 1 , 0 , - 2 ² + t ± 1 , 2 , 2 ² Find the coordinates of the point where this line intersects the y -axis. 5. There is a plane that contains the y -axis as well as every point on the line described in problem 4. Find the equation of this plane.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Assignment 4. Vector Functions and Space Curves Read 14.1 - 14.4 You should be able to do the following problems: Section 14.1/Problems 7 - 34 Section 14.2/Problems 1 - 29, 31 Section 14.3/Problems 1 - 6 Section 14.4/Problems 3 - 16, 33 - 38
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 03/20/2011 for the course MA 243 taught by Professor Poon during the Spring '09 term at Embry-Riddle FL/AZ.

### Page1 / 17

hw243 - MA 243 Calculus III - Spring 2011 Assignments...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online