#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: Issac Newton, Albert Einstein

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

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


##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)

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

{Dist (A,B), Dist(B,C), Dist(A,C)}
{sqrt(2)}
#equalateral

#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]
#r1(t)=r2(t):=[t+1=2t,2t=t+1,3t=3t]
#r1(t)=r2(t):=[1,1,1]
Lines do meet