#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) The distance of |PQ| is square root of (1^2+1^2)=square root of 2 The distance of |QR| is square root of (1^2+1^2)=square root of 2 The distance of |RP| is square root of (1^2+1^2)=square root of 2 So, the three sides of triangle PQR are equal, which means triangle PQR is an quilateral 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) [1,0,0]+t*[1,2,3]=[0,1,0]+t*[2,1,3] [1,-1,0]=t*[1,-1,0] t=1 so, these two lines meet at (1,[2,2,3])