#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 calculs?:
# Deep learning and neural nets

# C. WHAT IS THE "DISTANCE" IN SPECIAL RELATIVITY?:   
# sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2 - c^2*(t2-t1)^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)

# distance PQ = sqrt((1-0)^2 + (0-1)^2 + (0-0)^2) = sqrt(1+1+0) = sqrt(2)
# distance PR = sqrt((1-0)^2 + (0-0)^2 + (0-1)^2) = sqrt(1+0+1) = sqrt(2)
# distance QR = sqrt((0-0)^2 + (1-0)^2 + (1-0)^2) = sqrt(0+1+1) = sqrt(2)
# all three sides have length sqrt(2) therefore it's equilateral



#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) = [t+1, 2t, 3t]
# r2(t) = [2t, t+1, 3t]
# eq := {2t=t+1, 3t=3t, t+1=2t}
# solve(eq, t)
# results in t=1

#The lines meet at t=1