1-Is there a plane that is perpendicular to the plane containing the point ?[AOBJ:8.5]

2-Draw a sketch of the planes corresponding to the equation .[AOBJ:8.6]

3.Describe the difference between the planes and .[COBJ:8.6]

4-Explain why the planes and never intersect. [COBJ:8.6]

5-a. A plane, , has as its Cartesian equation. Determine the Cartesian equation of a plane that is perpendicular to and contains the point .[AOBJ:8.5]

b. Determine the Cartesian equation of a plane that containsPand is parallel to .

6-A plane is defined by the Cartesian equation .[COBJ:8.5]

a. What is a normal vector for this plane?

b. Does this plane pass through the origin? If not, determine a plane that is parallel to the given plane that does pass through the origin.

c. Write the coordinates of three points on the given plane.

7. a. Determine the Cartesian equation of a plane that hasx-, y-,andz-intercepts , 1, and , respectively.[COBJ:8.6]

b. Draw a sketch of the plane in part a.

8. Describe the following planes in words. [COBJ:8.6]

a.

b.

c.

9. a. Determine one equation that describes the graph of the two planes and .[COBJ:8.6]

b. Determine the intersection of the planes given in part a.

10. a. Determine the vector equation of the line of intersection of the plane and thexy-plane.[T/IOBJ:8.6]

b. Determine the vector equation of the line of intersection of the plane and theyz-plane.

c. Draw a sketch of the plane .