Math 427L Week 1

A. M and T problems:

1.1 / 6, 9, 14, 16, 221.2 / 11, 12, 13, 141.3 / 4, 6, 13, 16c, 25

B. Stewart problems:none

C. Warm-up problems:

Let a = (1; 2; 3) and b = (3;1; 4) be vectors and P (4;2; 1); Q(3; 0; 5); and R(1; 1; 1) be pointsin (R)3.

1. Find projab.

2. Findjja bjj:3. Find the parametric equations of the line through P and Q.

4. Find the equation of the plane through P;Q and R.

5. Find the angle between a and b.

D. Hand-in Problems:

1. Use projections to nd the distance from E(7; 4;1) to the plane dened by F (3; 2; 1), G(2;2; 2)and H(1; 0; 1).

2. A spaceship from Earth travels along the path r(t) = (2; 1; 3)t + (6;2; 1): A spaceship fromUranus travels along the path s(t) = (6;3; 3)t+ (4;1;8). At what point do the paths of thespaceships intersect? Do the spaceships crash?

3. Show that for vectors a, b and c we have (a b) c = (a c)b (b c)a.4. Find the distance from the point A(5;1; 2) to the line traveled by the spaceship from Uranusin problem 2.