1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Vector Subtract Given Magnitude

  1. Dec 17, 2017 #1
    1. The problem statement, all variables and given/known data
    Let's say i was given Vector A and B. The Angle between them is 60 degrees. Vector A's magnitude is 40 and Vector B's magnitude is 50. Find magnitude of vector C, if C = vector A - vector B.

    2. Relevant equations
    I'm given the magnitudes, and need to find magnitude of C

    3. The attempt at a solution
    I'm kinda confused cause I dont think this is a simple problem. But, I thought that magnitude of C would be 10. Since A-B = -10 , and 10 is the magnitude
     
  2. jcsd
  3. Dec 17, 2017 #2

    George Jones

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Can you draw a diagram for the situation?
     
  4. Dec 17, 2017 #3
    upload_2017-12-17_23-38-33.png
     
  5. Dec 17, 2017 #4

    Delta²

    User Avatar
    Homework Helper
    Gold Member

    By which side of the triangle the vector A-B is represented? What do you get if you properly use law of cosines?
     
  6. Dec 17, 2017 #5
    Magnitudes don't add that way unless the vectors are parallel and so you need to solve the triangle using the law of cosines.

    For example, if the angle between A and B were 0, then by the law of cosines

    [tex]c^2=a^2+b^2-2ab\cos{(0)}= (a-b)^2
    \\
    c = |a-b|

    [/tex]

    Which is what you tried to do but the angle is not zero in this case which is why it's wrong
     
  7. Dec 17, 2017 #6
    Thanks. I definitely did not learn this from my physics class.
     
  8. Dec 24, 2017 #7
    I thought of this problem as C = A + (-B). This means that it is the same as adding a vector, just the vector you are adding is negative. In order to add the vectors, we must split them into their components. We know that vector A is at an angle of 60 and therefore has X and Y components, while B is parallel to the horizontal and only has an X component equal to its magnitude.

    To split vector A, we use Cos and Sin to find the vertical and horizontal components of the vector.
    X Component (horizontal): Cos(60)*40=20
    Y Component (vertical): Sin(60)*40=34.64

    Now that we know the vertical and horizontal components of vector A, we can add the corresponding components of B, although since we are ultimately subtracting B from A, we just make B negative.

    This leaves us with:
    X: 20 + (-50) = -30
    Y: 34.64 + 0 = 34.64

    Then we use the Pythagorean theorem to find the result vector of these new horizontal and vertical components
    (A*A) + (B*B) = (C*C) = √(-30*-30) + (34.64*34.64) = C
    C = 45.83

    We know that the resultant vector has a magnitude of 45.83.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted