#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?: 


##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)
#P:=[1,0,0]
#Q:=[0,1,0]
#R:=[0,0,1]

#Dist(P,Q); =sqrt(2)
#Dist(P,R); =sqrt(2)
#Dist(Q,R); =sqrt(2)

#{Dist(P,Q),Dist(P,R),Dist(Q,R)}; =sqrt(2)

#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]=[1+t,2t,3t]

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

# Must get r1(t)=r2(s)

#1+t=2s, 2t=1+s, 3t=3s

#3t=3s -> s=t -> t=1 also 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 lines meet at (2,2,3)