# Thread: Vector in ai+bj Form

1. ## 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

2. 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.

$\displaystyle <a,b>=a\mathbf{i}+b\mathbf{j} \implies <7,-3>=7\mathbf{i}-3\mathbf{j}$

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

Its magnitude is: $\displaystyle \sqrt{(c-a)^2+(d-b)^2}$.

4. 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.

5. 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.

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

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