Use a computer to investigate this family of surfaces

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Unformatted text preview: f the graph depend on the numbers a and b? x 2 y 2 c xy. In particular, you should determine the transitional values of c for which the surface changes from one type of quadric surface to another. 2. Use a computer to investigate the family of surfaces z 3. Members of the family of surfaces given in spherical coordinates by the equation 1 0.2 sin m sin n have been suggested as models for tumors and have been called bumpy spheres and wrinkled spheres. Use a computer to investigate this family of surfaces, assuming that m and n are positive integers. What roles do the values of m and n play in the shape of the surface? |||| 13 Review ■ CONCEPT CHECK ■ 1. What is the difference between a vector and a scalar? 12. How do you find the angle between two intersecting planes? 2. How do you add two vectors geometrically? How do you add 13. Write a vector equation, parametric equations, and symmetric them algebraically? 3. If a is a vector and c is a scalar, how is c a related to a geo- metrically? How do you find c a algebraically? 4. How do you find the vector from one point to another? 5. How do you find the dot product a b of two vectors if you know their lengths and the angle between them? What if you know their components? 6. How are dot products useful? 7. Write expressions for the scalar and vector projections of b onto a. Illustrate with diagrams. 8. How do you find the cross product a b of two vectors if you know their lengths and the angle between them? What if you know their components? 9. How are cross products useful? 10. (a) How do you find the area of the parallelogram determined by a and b? (b) How do you find the volume of the parallelepiped determined by a, b, and c? 11. How do you find a vector perpendicular to a plane? equations for a line. 14. Write a vector equation and a scalar equation for a plane. 15. (a) How do you tell if two vectors are parallel? (b) How do you tell if two vectors are perpendicular? (c) How do you tell if two planes are parallel? 16. (a) Describe a method for deter...
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This note was uploaded on 02/04/2010 for the course M 56435 taught by Professor Hamrick during the Fall '09 term at University of Texas.

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