**Math 3592H Honors Mathematics I Fall Semester 2008
**

Exercises:

Further questions on Section 1.4: 16, 17

Let P1 be the plane x + 2y + 3z = 4 and let P2 be the plane x - y + z = 6.

1. Find the angle between P1 and P2.

2*. Find a vector which has the same direction as the line of intersection of P1 and P2.

3*. Find the equations of the line of intersection of P1 and P2 in the form

(x-a)/u = (y-b)/v = (z-c)/w

4*. Find the shortest distance from the point (1,1,1) to the plane P1.

5*. Find the equation for the plane which passes through the point (2,3,5) and is perpendicular to the vector (-1,4,1).

6. Find the shortest distance between the line x-1 = 2y-4 = z+1 and the line 3x+1 = y-1 = 2z-1.

(and also if we get to the end of section 1.5: 8, 9, 10 (assume 9 without proof),19, 21a, 22, 23c, 23e).

Last week I set homework questions too far ahead in the book for what eventually we covered in class. This week I am hoping I guess better. We will be doing some extra things along the lines of the extra questions 1 - 6 above, and then I am hoping we will get up to page 97. The questions listed in parentheses for section 1.5 go beyond this. Ignore them if we do not get beyond page 97.