#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: Einstein, Archimedes,Newton 

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

# C. WHAT IS THE "DISTANCE" IN SPECIAL RELATIVITY?: ((x2-x1)^2+(y2-y1)^2+(z2-z1)^2)

##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];
#make sure distance from P to Q=distance from Q to R=distance from R to P
#PQ=sqrt(2),QR=sqrt(2),RP=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)
#basically you set the two equations equal to each other, if they equal then they meet if not then they don't meet
#in this case they don't meet