#Sai Embar
#Ok to post
  
#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, Isaac Newton, Albert Einstein

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

Deep Learning

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

Not in the lecture, you forgot to tell us

##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([1,0,0],[0,1,0]) = sqrt((1-0)^2+ (0-1)^2+ (0-0)^2);
sqrt(2)
#Dist([0,1,0],[0,0,1]) = sqrt((0-0)^2+ (1-0)^2+ (0-1)^2);
sqrt(2)
#Dist([1,0,0],[0,0,1]) = sqrt((1-0)^2+ (0-0)^2+ (0-1)^2);
sqrt(2)

The distance between all points are equal to sqrt(2) which means that it 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)


not sure what t means here.