#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: N/A

# B. WHAT BRANCH OF AI USES Multivariable calculus?: N/A

# C. WHAT IS THE "DISTANCE" IN SPECIAL RELATIVITY?: N/A


##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(Q[1]-P[1]^2 + Q[2]-P[2]^2 + Q[3]-P[3]^2) = sqrt(1)
#Dist(P,R) := sqrt(R[1]-P[1]^2 + R[2]-P[2]^2 + R[3]-P[3]^2) = sqrt(1)
#Dist(Q,R) := sqrt(R[1]-Q[1]^2 + R[2]-Q[2]^2 + R[3]-Q[3]^2) = sqrt(1)
#{Dist(P,Q); Dist(P,R); Dist(Q,R)} = {sqrt(1)}
#Using the distance formula between different variations of pairs of the three points,
#it is clear that all of the points are equidistant, creating an equilateral Triangle

#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)

#L1(t):= [1,0,0]+ t*([1,0,0]-[1,2,3]);
# L1(t):= [1+t,-2t,-3t];
#L2(s)=[0,1,0]+ s*([0,1,0]-[2,1,3]);
# L2(s)= [-2s,1+s,-3s];
#eq := (L1[1]:=L2[1], L1[2]:=L2[2], L1[3]:=L2[3]);
#eq := (1+t:=-2s, -2t:=1, -3t:=-3s);
#eq := (2=2, 2:=2, 3:=3);
# I used the equation PQ=(Q-P) * t;
# Letting t=0 and s=0 shows that the two lines meet at point [2,2,3]