#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?:   

	I do not recall you talking about these topics in the lecture.


##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 P and Q, Q and R, P and R is sqrt(2), which could be found using the distance formula.
	sqrt((x1-x2)^2 + (y1-y2)^2 + (z1-z2)^2)
	Since all the distance between the points are the same, this 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)

	Multiply t and [1,2,3] and get [t,2t,3t].
	Add this to [1,0,0] and you will get r1(t)=[1+t,2t,3t] 

	Multiply t and [2,1,3] and get [2t,t,3t].
	Add this to [0,1,0] and you will get r2(t)=[2t,1+t,3t] 
	
	To find a intersection, we need to set r1(t) and r2(t) as equals.
	[1+t,2t,3t] = [2t,1+t,3t]
	This is the same as...
	[1+t=2t, 2t=1+t, 3t=3t]
	r1(1) = r2(1)	

	Therefore, when t=1, the functions intercect.