Math 260

Exam 1

 

  1. Let  and . Find:

a)

b)

c) The angle between and

d) The area of the triangle with vertices (0,0,0), (1,-2,2), and (3,0,-4).

 

  1. Find the line through the points (9,-2,4) and (3,2,-1).
  2. Find the plane containing the line from problem 2 and the point (0,2,0).
  3. A particle moves in space along the path

a)      Find the tangent line to the path at (4,2,-6).

b)      Find the speed of the particle. What is the minimum speed?

c)      Find the curvature of the path.

  1. What is the maximum curvature of the function
  2. The point (2,p/4,p/3) is given in spherical coordinates. Find the cylindrical and rectangular coordinates.
  3. (Extra credit)

a)      Show that if y=f(x) has 0 curvature, then it is a line.

b)      Find the intersection line for the planes x+y=0 and 2x-z=0.