Vector points given another point

[EulersNumber]

Hello,

I have perhaps an odd question, but, if I have a vector described by <5, 4> and I have another vector that begins at teriminal end of that vector <5, 4> that points west of north from that point and thus its arrow (I apologize, I think its called the tail but not 100% sure) is closer to x=0, then I am right in thinking finding the x coordinate is just magnitude times cos theta and the y coordinate is magnitude times sin theta plus 4? I want to say the reason that is right is due to the unit circle and vectors have a directionality to them, but I'm not quite sure.

Many thanks in advance!

 

[mario99]

Let us call the first vector [imath]\bold{A} = \ <5,4>[/imath] and the second vector [imath]\bold{B}[/imath]

Because [imath]\bold{B}[/imath] is going west of north, its components are:

[imath]\bold{B} = \ <-B_1,B_2> \ = \ <-B\sin\theta, B\cos\theta>[/imath]

The angle [imath]\theta[/imath] here is between [imath]\bold{B}[/imath] and the [imath]\text{y-axis}[/imath]

If we add them, for example we will get:

[imath]\bold{A} + \bold{B} = \ <5 - B\sin\theta, 4 + B\cos\theta> [/imath]

If vector [imath]\bold{B}[/imath] goes north of west, its components will be:

[imath]\bold{B} = \ <-B_1,B_2> \ = \ <-B\cos\theta, B\sin\theta>[/imath]

The angle [imath]\theta[/imath] here is between [imath]\bold{B}[/imath] and the [imath]\text{x-axis}[/imath]

 

[Harry_the_cat]

I would strongly recommend you draw a diagram.