#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 Neutral Nets

# C. WHAT IS THE "DISTANCE" IN SPECIAL RELATIVITY?: sqrt(x^2+y^2+z^2-c^2*t^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 given vertices will form an equilateral triangle as the three sides are of the same length.
The distance between P and Q is sqrt{(1^2)+(1^2)} which is sqrt of 2.

The distance between Q and R is sqrt{(1^2)+(1^2)} which is sqrt of 2.

The distance between P and R is sqrt{(1^2)+(1^2)} which is sqrt of 2.
Therefore its a 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)

#r1(t)=[1,0,0]+ t*[1,2,3]=[1,0,0]+ [t,2*t,3*t]=[1+t,2*t,3*t]
#r2(s)=[0,1,0]+ s*[2,1,3]=[0,1,0]+ [2*s,t,3*s]=[2*s,1+s,3*s]
#Since we need to know where r1 and r2 meet, we place them equal to each other.
#Therefore, 1+t=2*s , 2*t=1+s , 3*t=3*s

The solutions are, t=1 and t=s.
r1(t=1)=[1+1,2*1,3*1]=[2,2,3]
r2(s=1)=[1+1,2*1,3*1]=[2,2,3]
Therefore they meet at [2,2,3].