#ATTENDANCE QUIZ for Lecture 1 of Math251(Dr. Z.)
#EMAIL RIGHT AFTER CLASS (OR RIGHT AFTER YOU WATCHED THE VIDEO) THE EDITED VERSION OF
#THIS .txt FILE (WITH YOUR ANSWERS)
#TO:
#DrZcalc3@gmail.com
#Subject: q1
#with an ATTACHMENT CALLED:
#q1FirstLast.txt
#(e.g. q1DoronZeilberger.txt)



#ANSWERS TO RANDOM FACTS IN THE LECTURE

# A. ACCORDING TO Dr. Z. THE TOP THREE SCIENTISTS OF ALL TIME ARE: 

# B. WHAT BRANCH OF AI USES Multivariable calculs?:

# C. WHAT IS THE "DISTANCE" IN SPECIAL RELATIVITY?:   

None were asked in the video.


##THE ACTUAL QUIZ:

#1. Show that the triangle with vertices 
#P=[1,0,0], Q=[0,1,0], R=[0,0,1]  is an equilateral triangle.


#YOUR SOLUTION HERE (EXPLAIN ALL THE STEPS)
The distance between point P and point Q is equal to the sqrt((1-0)^2+(0-1)^2+(0-0)^2) which equals sqrt(2).
The distance between point Q and point R is equal to the sqrt((0-0)^2+(1-0)^2+(0-1)^2) which equals sqrt(2).
The distance between point R and point P is equal to the sqrt((0-1)^2+(0-0)^2+(1-0)^2) which equals sqrt(2).
Since all distances between each pair of points are equal to sqrt(2), the triangle must be an equilateral triangle. 




#2.  Determine whether the following two lines ever meet.
#If they do meet, where?

#r1(t)=[1,0,0]+ t*[1,2,3]

#r2(t)=[0,1,0]+ t*[2,1,3]

#YOUR SOLUTION HERE(EXPLAIN ALL THE STEPS)
r1(t)=[1,0,0] + t*[1,2,3] = [1,0,0] + [t,2t,3t] = [t+1,2t,3t]
r2(s)=[0,1,0] + s*[2,1,3] = [0,1,0] + [2s,s,3s] = [2s,s+1,3s]

r1(t) = r2(s)
t+1 = 2s, 2t = s+1, 3t=3s
t=1, s=1

r1(1)=[1+1,2(1),3(1)]=[2,2,3]
r2(1)=[2(1),1+1,3(1)]=[2,2,3]

The two lines will meet at point (2,2,3).