Question

vectors,

Can someone please help me with the very first one only ? Just so that I can get the hang of it.

http://screencast.com/t/hjMSzGHhg

Answer 1

okay so b=<1,1>
ill use this notation so its a beat cleaner, it means the same thing i+j

Answer 2

bit*

Answer 3

ok

Answer 4

any vector parallel to b must be of the form
k*<1,1> = <k,k>
and vector perpendicular to this is of the form <-1,1> or <1,-1>
so t*<-1,1> = <-t,t>

now we add these to to get our vector
<-t,t> + <k,k> = <2,-4>
vectors add compnents by component is add and js add
<-t+k,t+k>=<2,-4>
therefore
-t+k=2
t+k=-4
solve this system of equations
k-t=2
k+t=-4
therefore
k=-1
t=-3

Answer 5

so we geet vectors
<k,k> and <-t,t> become
<-1,-1> , <3,-3>

Answer 6

2i-4j=x(i+j)+y(-i+j),where x and y are scalars.
2i-4j=(x-y)i+(x+y)j
x-y=2
x+y=-4
find x and y