Adding Vectors: Understanding Direction and Length

[aatari]

Homework Statement

Hi Guys, I am a bit unclear regarding adding vectors and hoping someone can clear up the confusion for me.

In the image below, we are adding two vectors and we used the vector components to find find x and y. Finally we then used x and y to get the resultant and the angle.

There is a diagram after "Now place the resultant components head-to-tail to form a right angled triangle", where we begin with x going east, then y going north and touching the tip of x.

My question is how do we determine to place the x and y in this way? Is there any criteria or methodology that we use because I could also place x starting at the tip of resultant vector and going east and then from the head of x vector going north to form y vector. If I do this the angle differs as adjacent and opposite sides of the angle change. Could anyone please help me understand this.

I hope my questions is clear.Problem: Determine the length and direction of a + b if a is 4 m [N30°E] and b is 2 m [S40°W].

Homework Equations

N/A

The Attempt at a Solution

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[Doc Al]

Is there any criteria or methodology that we use because I could also place x starting at the tip of resultant vector and going east and then from the head of x vector going north to form y vector.

It doesn't matter whether you place the start of the y component vector at the tip of the x component vector (not the resultant vector!), or the reverse. You get the same answer either way.

If I do this the angle differs as adjacent and opposite sides of the angle change.

Try again. If you get different resultant vectors, you're doing something wrong. (Note that the triangle you get might be different, but the resultant vector will be the same.)

 

[.Scott]

My question is how do we determine to place the x and y in this way? Is there any criteria or methodology that we use because I could also place x starting at the tip of resultant vector and going east and then from the head of x vector going north to form y vector. If I do this the angle differs as adjacent and opposite sides of the angle change. Could anyone please help me understand this.

I'm not sure I understand your question, but the key here is to combine the x and y vectors. You have a y component that is positive 1.93, towards the North. You have a positive 0.71 x component, towards the East. So whether you put the x arrow down and then place the tail of the y with the head of the x, or you put the y arrow down first and then place the x at its end, you still end up in the same place. That same place is 1.93 to the North and 0.71 to the East of where ever you started from. Also, in either case, once you draw the resultant arrow, you will have a right triangle and you will be able to use their formula to compute the length of that arrow (2).

However, if you use the different triangle, you'll be looking at a different angle. Instead of computing 20 degrees east of north (as shown in the example) you could end up with 70 degrees north of east. But that would just be an alternate way of specifying the same bearing.

 

[aatari]

It doesn't matter whether you place the start of the y component vector at the tip of the x component vector (not the resultant vector!), or the reverse. You get the same answer either way.Try again. If you get different resultant vectors, you're doing something wrong. (Note that the triangle you get might be different, but the resultant vector will be the same.)

Your are right, resultant does not change. However, my angle changes.

 

[aatari]

However, if you use the different triangle, you'll be looking at a different angle. Instead of computing 20 degrees east of north (as shown in the example) you could end up with 70 degrees north of east. But that would just be an alternate way of specifying the same bearing.

So my answer will still be correct?

 

[Doc Al]

However, my angle changes.

The angle of your triangle changes. But the angle that the resultant makes with the horizontal and the vertical does not. You may have to convert one to the other.