#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:

    #Arcchimedes, Isacc Newton, Albert Eistein

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

    #Deep Learning. Go (difficult game). 

# 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)

    #We must find the distance for PQ, PR, and QR. 
    #Distance of PQ is sqrt(2)
    #Distance of PR is sqrt(2)
    #Distance of QR is also sqrt(2)
    #Because all the distances are equal, the triangle is 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)

    #Expand the equations
    #r1(t) = [t+1, 2t, 3t]
    #r2(t) = [2t, t+1, 3t]
    #Set them equal to each other: 
    #[t+1 = 2t, 2t = t+1, 3t = 3t]

    #At both x and y, they meet at x=1 and y=1. However, z can be any value.