Math 251                         Name______KEY_________
Quiz 1
  1. Fully describe in words the 3-dimensional region represented by the equation or inequality.

    2.  

     
     
     
     
     

    1. z > 4

      2.  

       
       
       
       
       

      This region is the half-plane that is above (and not including)
      the plane z=4,which is the plane parallel to and 4 units above
      the xy-plane


       

    2. (x-2)2+y2+(z+5)2=9

      3.  
      This is a sphere of radius 3 units centered at (2,0,-5).

       


       

    3. y2+z2=9


      4. This is a circular cylinder with radius 3 units.  It wraps around
      the x-axis and extends infinitely.

     
    2. Find the distance from the point (-2,3,4) to each of the following:
     
    1. The yz - plane.


      2. This is the same as asking how far out the point is in
      the positive or negative x-direction.  So the distance
      is the absolute value of the x-coordinate, in this case
      that is 2 units.

      Another way to complete this problem is to realize
      that the point on the yz-plane that is closest to the
      given point is (0,3,4).  you can then compute the
      distance between the two points, which is 2 units.
       

    2. The z - axis.


      3. The point on the z-axis that is closest to the given point
      is (0,0,4).  We use the distance formula:
      d= sqrt{(-2-0)^{2}+(3-0)^{2}+(4-4)^{2}}= sqrt{13}units.

File translated from TEX by TTH, version 2.92.
On 11 Sep 2001, 11:02.