# Vector in ai+bj Form

• May 25th 2011, 03:31 PM
IDontunderstand
Vector in ai+bj Form
Find a vector determined by the two points in ai+bj form and then find its magnitude.

(-3,1) and (4,-2)

(4,7) and (0,5)

I have no idea where to start. All I know is that a=<1,0> and b=<0,1>

I think that I want to find the ordered pair/component form of the vector
1) which will be <7,-3>.

Do I find the magnitude of that vector? (Squrt(58))

I do not know what to do know. I get stuck here if the first part is correct and I am not sure if that is correct.

Thank you
• May 25th 2011, 03:35 PM
TheEmptySet
Quote:

Originally Posted by IDontunderstand
Find a vector determined by the two points in ai+bj form and then find its magnitude.

(-3,1) and (4,-2)

(4,7) and (0,5)

I have no idea where to start. All I know is that a=<1,0> and b=<0,1>

I think that I want to find the ordered pair/component form of the vector
1) which will be <7,-3>.

Do I find the magnitude of that vector? (Squrt(58))

I do not know what to do know. I get stuck here if the first part is correct and I am not sure if that is correct.

Thank you

Your answer for the first part is correct you just need to sort out the notation.

$=a\mathbf{i}+b\mathbf{j} \implies <7,-3>=7\mathbf{i}-3\mathbf{j}$
• May 25th 2011, 03:49 PM
Plato
Quote:

Originally Posted by IDontunderstand
Find a vector determined by the two points in ai+bj form and then find its magnitude.

Suppose we have two points: $(a,b)~\&~(c,d)$
The vector determined by the two points in ai+bj form is:
$(c-a)\mathbf{i}+(d-b)\mathbf{j}$.

Its magnitude is: $\sqrt{(c-a)^2+(d-b)^2}$.
• May 25th 2011, 03:49 PM
IDontunderstand
So all I have to do is add a i and j after I find the component? My book shows finding a unit vector before it talks about ai+bj form but does not give an example after it.
• May 26th 2011, 05:24 AM
HallsofIvy
Quote:

Originally Posted by IDontunderstand
So all I have to do is add a i and j after I find the component?

You also said in your first post "All I know is that a=<1,0> and b=<0,1>". That's part of your confusion- if you write a vector in the form "ai+ bj" is it i that is <1, 0> and j that is < 0,1>, not a and b. a and b are numbers- they are the "components", not the unit vectors.

Quote:

My book shows finding a unit vector before it talks about ai+bj form but does not give an example after it.