Math 3592H Honors Mathematics I Fall Semester 2008

Assignment 3 - Due Thursday 9/25/2008

Read: Hubbard and Hubbard Section 1.5, probably only to page 97.

Exercises:
Hand in only the exercises which have stars by them.

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.

Section 1.5: 1, 2, 3, 4*, 5, 6*, 12, 13, 14*, 15,
(and also if we get to the end of section 1.5: 8, 9, 10 (assume 9 without proof),19, 21a, 22, 23c, 23e).