#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: archimedes, newton, Einstein 

# B. WHAT BRANCH OF AI USES Multivariable calculus?: deep learning, (Go!), neural nets

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


##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)

#because the distance between all three points (sqrt(2)) this means sidelengths are equivalent.

#sqrt( (x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2 )

#We use this formula for all three points.



#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)