#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)

Suhayb Islam

#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(x^2+y^2+z^2)-x^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)

Equilateral Triangle = one where all the sides are the same length. 
Dist(a, b) AND Dist(a, c) AND Dist(b, c) are all sqrt(2). They are all the same.
This is why those vectors create 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)

We need to make sure that the equations have the same output for the same input at some point in order to ensure they intersect.
1+1t = 2s
+2t = 1+s
+3t = +3s

Take a pair and Solve System of Equations
t=1, s=1
2 = 2 for first equation
2 = 2 for second equation
3 = 3 for third equation

Yes, they intersect at (1, 1)