How Do You Correctly Add and Subtract Multiple Vectors?

[k-rod AP 2010]

Homework Statement

vectorA: 6 @ 40^o, vectorD: 2 @ 90^o, vectorB: 10 @ 80^o

i have to do this problem: vectorA + vector D - vectorB

Homework Equations

The Attempt at a Solution

i had found the components to these vectors in previous problems to be:
vectorA: x=4.01 y=4.46 vectorD: x=0 y=2 vectorB: x=9.85 y=1.74

i added the total x and total y for all the vectors:
total x: (4.01+0+ -9.85)=-5.84 total y:(4.46+2+ -1.74)=4.72

i made the components for the vectorB negative because they were being subtracted but i am not sure if this is the proper procedure

these are the resultant calculations based off of the x and y totals
resultant magnitude: root((-5.84)^2 + (4.72)^2)= 7.51m
resultant angle: arctan(4.72/-5.84)=-38.9^o

Did i follow the proper procedure to add and subtract vectors in the same problem?

 

[The legend]

the procedure looks right to me... i haven't checked the calculations.

 

[zgozvrm]

Your procedure is right, but some of your calculations are incorrect.
The components of vector A are off
The components of vector D look good
The components of vector B are reversed

 

[k-rod AP 2010]

Its my first year in physics so i am not the best at it but thanks for the confirmation. i thought it was right but i wasnt sure.

and zgozvrm, u were right about my numbers, i was doing the problem in a rush so i must have reversed them, my bad.

 

[rwisz]

Yes, your procedure for adding and subtracting vectors is correct. To add or subtract vectors, you need to break them down into their components and then add or subtract the corresponding components. In this case, you correctly added the x and y components of the vectors and then found the magnitude and angle of the resultant vector using the Pythagorean theorem and inverse tangent function. Additionally, you correctly made the components of vector B negative when subtracting it from the other vectors. Overall, your approach is correct and your calculations are accurate.