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: Basic Vectors: If vector A and C are given what is the magnitude of vector B?

  1. Sep 1, 2011 #1
    Vector A has a magnitude of 14.0m and is angled 38.0 degrees counterclockwise from the +x direction. Vector C has a magnitude of 13.2m and is angled at 22.4 degrees counterclockwise to the -x direction. If vector A + vector B = vector C what is (a) the magnitude (b) and angle - relative to +x direction - of vector B? State your angle as a positive number.

    (a) 26.9m
    (b) 210 degrees

    Relevant equations:
    I will use vA as a shorthand to represent vector A and ||vA|| to represent the magnitude of vector A.

    Ax = ||vA||cos(theta)
    Ay = ||vA||sin(theta)
    ||vA|| = sqrt(Ax^2 + Ay^2)


    My reasoning was that if I could find the vectors of vA and vC I could subtract vA from vC to obtain the vector vB.

    vA + vB = vC
    vB = vC - vA = <Cx-Ax, Cy-Ay> = <Bx, By>

    From there I would use the equation for the magnitude of the vector to obtain the answer for part a.

    ||vB|| = sqrt(Bx^2 + By^2)

    However, when I plug in the numbers I keep getting the incorrect answer, 23.5m.

    Ax = 11.0m Ay = 8.62m vA = <11.0m, 8.62m>
    Cx = -12.2m Cy = 5.03m vC = <-12.2m, 5.03m>
    vB = <-12.2m-11.0m, 5.03m-8.62m> = <-23.2m, -3.59m>
    ||vB|| = sqrt((-23.2^2 + (-3.59)^2)) = sqrt(551.13) = 23.5m

    I haven't attempted part (b) yet due to the fact that there is an error to the first part of the question. What did I do wrong? I felt fairly confident in what I was doing and have been stumped on this question for nearly an hour. Thank you in advance for reading my problem.
    Last edited: Sep 1, 2011
  2. jcsd
  3. Sep 1, 2011 #2


    User Avatar
    Homework Helper


  4. Sep 1, 2011 #3
    It gave me the right answer! Amazing! But, how did you get the negative? In my calculator sin(157.6) = 0.38. Multiply that by 13.2 and I got 5.03. Where did the negative come from?
  5. Sep 2, 2011 #4


    User Avatar
    Homework Helper

    The angle is not 180-22.4 but 180+22.4. It is counter clockwise to the -x direction, in the third quadrant.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook