Vector
Projection from a point to plane
Magnitude of a vector
Distance from the point P(x,y,z) to the plane of A,B,C
Unit or Length of a Vector
ARC LENGTH
Direction as well
Midpoint Formula
L=
Distance Formula
M= d=
Vector Projection
Normal Vector of CAB
Math 228 Section 1 and 4
HW 2
B-level problems
1. Suppose u, v, and w are vectors in 3-space with u 6= 0:
(a) Show by example that u
(b) Suppose u
v=u
v=u
w does not imply v = w?
w and u v = u w: Must v = w? Support your answer.
2. Let v =<a; b; c> be a v
Math 228 Sections 1 and 4
Written Assignment 3
Due 9/25
B Level Problems
1. Suppose a particle moves in space with its position vector at time t given by r (t) = f (t)i+g(t)j+h(t)k,
a < t < b: Denote the particle velocity at time t by v (t) :Assume that t
Math 228 Sections 1 and 4
HW 4
Due Friday, October 11
Poorly written homework will not be graded.
B1. (3 pts) Carefully sketch on the same axes the surfaces x2 + y 2 z 2 = 1 and x = 1: Also sketch the
intersection curve and nd the equations that describe
Math 228 Section 1 and 4
Written Assignment 1
The due date for this assignment is Monday September 9
B. 1. Find in simplied form the equation that describes all points(x; y; z) that are
equidistant from (1; 2; 1) and (2; 4; 5). What kind of geometric gure
Math 228 Sections 1 and 4
Assignment 5AB
Due 10/21
B Level Problems
1. Section 14.4 # 44(b,c,d)
2. (Strange Saddle) Let f (x; y) = (y
x2 )(y
x4 ):
(a) Verify that (0; 0) is a critical point for f and that the discriminant at (0; 0) is zero.
(b) Verify tha