#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 calculus?:
# Deep Learning

# C. WHAT IS THE "DISTANCE" IN SPECIAL RELATIVITY?:
# ... I didn't catch it haha   


##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 each point should all be equal

#(Using Maple) Defining the variablesc
P:=[1,0,0]; Q:=[0,1,0]; R:=[0,0,1];

#Find distance between each point
Distance(P,Q);
 = sqrt(2)
Distance(Q,R);
 = sqrt(2)
Distance(R,P);
 = sqrt(2)

#Distances are all equal. Therefore, the triangle has equal sides
#and it is equilateral.

#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)
#(Using Maple) Define the variables
r1:= expand([1,0,0]+ t*[1,2,3]); r2=expand([0,1,0]+ t*[2,1,3])
                    r1 := [t + 1, 2 t, 3 t]

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

#Set lines equal to each other
eq:={L1[1]=L2[1], L1[2]=L2[2], L1[3]=L2[3]};
	eq := {2*t = r2[2], 3*t = r2[3], t + 1 = r2[1]}
solve(eq,t);

#When prompted to solve, Maple does not return a solution.
#Therefore, there is no solution and the lines do NOT intersect.