#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

# 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)
#dist(P,Q) = sqrt( (P[1]-Q[1])^2 + (P[2]-Q[3])^2 + (P[3]-Q[3])^2 )
#dist(P,Q) = sqrt( (1-0)^2 + (0-1)^2 + (0-0)^2 )
#dist(P,Q) = sqrt(2)

#dist(P,R) = sqrt( (P[1]-R[1])^2 + (P[2]-R[3])^2 + (P[3]-R[3])^2 )
#dist(P,R) = sqrt( (1-0)^2 + (0-0)^2 + (0-1)^2 )
#dist(P,R) = sqrt(2)

#dist(Q,R) = sqrt( (Q[1]-R[1])^2 + (Q[2]-R[3])^2 + (Q[3]-R[3])^2 )
#dist(Q,R) = sqrt( (0-0)^2 + (1-0)^2 + (0-1)^2 )
#dist(Q,R) = sqrt(2)

#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)

#To check if the two lines meet we must set them equal to each other:
#r1(t) = r2(t)
#[1,0,0] + t*[1,2,3] = [0,1,0] + t*[2,1,3]
#[1,0,0] + [t,2t,3t] = [0,1,0] + [2t,t,3t]
#[1+t,2t,3t] = [2t,1+t,3t]
#[1+t=2t, 2t=1+t, 3t=3t]
#[t=1,t=1,t=ANYTHING]
#These two lines meet when x=1,y=1 and z has infinitely many solutions in the [x,y,z] #format