Multivariable Calculus (Math 214) Assignment

due September 22, 1999

Please note that this course will meet Friday, September 17, but will not meet on Monday, September 20, nor on Tuesday, September 21.

There will be a quiz on Friday, September 17.

1. Let P and Q be the points in Cartesian 3-space given by

   P = (2, -3, 5) , and Q = (0, 1, -1) ,

   and let L be the line through P and Q.

   1. Find a parametric representation for the line L, i.e., find points A and B such that L consists of the points tA + B as t varies through the set of real numbers.

   2. Are either of A or B points on the line L?

   3. In your parametric representation of L, which values of the parameter t correspond to points on the line segment between P and Q ?

   4. Find the equations of two different planes that contain the line L.

2. Let L be the line passing through the point P = (1, -3, 2) that is perpendicular to the sphere

   x^{2} + y^{2} + z^{2} = 14

   at the point P.

   1. Identify two distinct points of L.

   2. Give a parametric representation of L.

   3. What is the equation of the plane through the point P that is perpendicular to the line L ?

   4. What is the equation of the plane that is tangent to the sphere at the point P ?