Change in Velocity: Find Solution and Reasoning

[yowatup]

Homework Statement

I am required to find the change in velocity given these two vectors:

Va = 4.4 m/s [E31*S]
Vb = 7.8 m/s [E25*N]

Homework Equations

delta V = Vb - Va
delta V = Vb + (-Va)

The Attempt at a Solution

I am stuck between two solutions:

#1. Simply subtracting the vectors:

V = Vb - Va
V = (7.8, 25*) - (4.4, 31*)
V = [7.1, 3.3] - [3.8, 2.3]
V = [3.3, 1.0]
V = (3.5, 16.8*)

#2. Reversing the direction of Va, its directionality becomes [W31*N], effectively 149*.

V = Vb + (-Va)
V = (7.8, 25*) + (4.4, 149*)
V = [7.1, 3.3] + [-3.8, 2.3]
V = (6.5, 59*)

Which solution is correct and why? The first would solution would be the same if you distributed -1 across to both terms, but I'm pretty sure that operation is not permitted.

 

[LowlyPion]

Doesn't taking the negative vector mean that the -31 is really 149 + 180 = 329

 

[yowatup]

I don't think so, as can be seen here:
http://i543.photobucket.com/albums/gg464/yowatupguystill/vector-1.jpg

EDIT: I might have been correct on my first attempt, but I had assumed that this was correct: https://www.physicsforums.com/archive/index.php/t-275728.html

 

[LowlyPion]

What is shown in your drawing is 329° and you are reversing it to 149° .

 

[yowatup]

Yes. Is that not correct, given that we are reversing the direction?

Secondly, I have just drawn out a vector diagram to scale of the vectors in question. It seems to support #2, though I'm not sure how certain to be - given that I haven't work graphically with vectors in a while.

 

[LowlyPion]

I believe Method 2 is the right way - the sum of the vector and the negative of a vector to do a vector subtraction..