#12.1  :

#5.
#The components of u is <x, tan45°x>=<x, x>

#7.
#The components of w is <x, -tan20° x,>=<x, -0.176x>

#9.
#The components of PQ is (Q1-P1, Q2-P2) = (-1,5)

#11.
#The components of PQ is (Q1-P1, Q2-P2)=(-2,-9)

#15.
#5(6,2)=(5*6,2*6)=(30,12)

#21 is on the PDF version

#41.
#ev=(3,4)/(sqrt(9+16))=(3/5,4/5)

#47.
#e=(a,tan4pi*a/7)/(sqrt((a*cos4pi/7)^2))=(4.494,-19.689)

12.2  : 

#11 is on the PDF version

#13.
#(a) 
#cos theta = (a1b1 + a2b2 + a3b3)/(|A||B|)=(8+32+72)/sqrt(16+64+144)sqrt(4+16+36)=1
#theta=0
#(a) Is parallel to v and in the same direction.

#(b) 
#cos theta = (a1b1 + a2b2 + a3b3)/(|A||B|)=((-4)+(-16)+(-36))/sqrt(16+64+144)sqrt(1+4+9)=-1
#theta=0
#(b) Is parallel to v and in the opposite direction.

#(c) 
#cos theta = (a1b1 + a2b2 + a3b3)/(|A||B|)=((-28)+(-112)+(-252))/sqrt(16+64+144)sqrt#(49+256+441)=-7sqrt(2611)/373
#theta does not equal to 0
#(c) Is not parallel to v.


#(d) 
#cos theta = (a1b1 + a2b2 + a3b3)/(|A||B|)=(24+80+168)/sqrt(16+64+144)sqrt(36+100+256)=17sqrt(7)/49
#theta does not equal to 0
#(d) Is not parallel to v.

#19
#-2<8,11,3>+4<2,1,1>=<-16,-22,-6>+<8,4,4>=<-8,-18,-2>

#25
#cos theta = (a1b1 + a2b2 + a3b3)/(|A||B|)=(8+(-2)+(-18))/sqrt(16+8+36)sqrt(4+1+9)=-sqrt#(210)/35
#theta does not equal to 0
#u Is not parallel to v.

#27
#cos theta = (a1b1 + a2b2 + a3b3)/(|A||B|)=((-18)+(-2)+32)/sqrt(9+1+16)sqrt(36+4+64)=3/13
#theta does not equal to 0
#u Is not parallel to v.

#31
#ev=<(-1)(-4,4,2)/sqrt(16+16+4)><2/3,-2/3,-1/3>

#49
#parametrization1: <5-0,5+2,2-1>=<5,7,1>
#Parametrization2: <5+0,5-2,2+1>=<5,3,3>

#51
#r1(t)=<4t-1,2-2t,2+t>
#r2(t)=<2t,1,1+t>
#[4t-1=2t, 2-2t=1 2+t=1+t]
#[2+t=1+t]
#[2=1]×
#t has no solution
#r1(t) and r2(t) do not intersect.