What Is the i,j Form of a Vector?

[HawKMX2004]

vector help asap please!

I have a problem that says define the i,j form of a vector and write the following vectors in i,j form u = P(1,1) to Q(2,4) and v = P(6, -3) to Q(7,0). I looked all through my book, and cannot find a definition for the i,j form of a vector ( i checked glossary, index,l and read the whole chapter again) I'm sure if i had a definition I could figure out how to re write the vectors...can anyone help please?

 

[dextercioby]

I don't know whether anyone can help,but hopefully i can.A vector in i+j form is expressed starting with its form in a basis.
Exempli gratia:
The vector $\vec{A}$ in the base $\vec{i},\vec{j}$has the form:
[tex]\vec{A}=5\vec{i}+7\vec{j} [/itex] <br /> ,so i step in and define its "i+j form" by the ordered pair:<br /> $$\vec{A}(\vec{i},\vec{j})=:(5,7)$$<br /> <br /> Using this simple example,try to solve your problem.<br /> <br /> Daniel.[/tex]

 

[HawKMX2004]

ok so for U for example, U in form i,j would be 1i + 1j and 2i + 4j ?? I am lost a little or does this mean 2i + 1i = 3 and 4j + 1j = 5 so U(i,j) = (3,5) ??

 

[HallsofIvy]

Do you have no idea at all what a vector is?

u is a vector from (1,1) to (2,4): The x component changes from 1 to 2 so it changes by 2-1= 1. The y component changes from 1 to 4 so it changes by 4-1= 3.
The "i" number is the x change and the "j" number is the y change:
u= 1i+ 3j (and that is NOT 4 anything!)

v runs from (6, -3) to (7,0). The x component changes from 6 to 7: it changes by 1. The y component changes from -3 to 0: it changes by 0-(-3)= 3.
v= 1i+ 3j (it's the same as u!)