#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:

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

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


##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)

If the triangle is an equilateral triangle, PQ = QR = RP

PQ = sqrt((1)^2 + (1)^2) = sqrt(2)
QR = sqrt((1)^2 + (1)^2) = sqrt(2)
RP = sqrt((1)^2 + (1)^2) = sqrt(2)

sqrt(2) = sqrt(2) = sqrt(2)
Therefore PQ = QR = RP, so the triangle 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)



r1 = [1 + 1t, 2t + 3t]
r2 = [2t, 1 + 1t, 3t]

If the lines meet, r1 = r2 at some value t

1 + 1t = 2t 
t = 1

2t = 1 + 1t
t = 1

3t = 3t
t = 1

The same value for t is achieved for all components of both lines, so r1 = r2 at t =1, so the two lines meet at t = 1.