#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)
The distance between P and Q= sqrt((Q[1]-P[1])^2+Q[2]-P[2])^2+Q[3]-P[3])^2)
			=sqrt(1+1+0)
			=sqrt2
The distance between R and Q= sqrt((Q[1]-R[1])^2+Q[2]-R[2])^2+Q[3]-R[3])^2)
			=sqrt(0+1+1)
			=sqrt2
The distance between R and P= sqrt((P[1]-R[1])^2+P[2]-R[2])^2+P[3]-R[3])^2)
			=sqrt(1+0+1)
			=sqrt2
Three distance are all: sqrt2
Therefore, P=[1,0,0], Q=[0,1,0], R=[0,0,1]  is 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)
expand r1(t)=[t+1, 2t, 3t];
expand r2(t)=[2t, t+1, 3t];
expand r1(t)=r2(t): [t+1=2t, 2t=t+1, 3t=3t];
Therefore, r1(t) and r2(t) meets at t=1.