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Vectors quantity

  1. Aug 31, 2015 #1
    1. The problem statement, all variables and given/known data
    Vector A has magnitude A = 4.0 units and is directed θA = 15◦ counterclockwise from the positive x-axis. Vector B has magnitude B = 4.0 units and is directed θB = 85◦ counterclockwise from the positive x-axis. Determine the following quantity: |A + B|^2 − |A − B|^2.


    2. Relevant equations


    3. The attempt at a solution
    Steps) 1. i calculated their components: Ax= 4.0 cos 15º = 3.86, Ay= 4.0 sin 15º = 1.04 , A= 4.898979486
    Bx= 4.0 cos 85º = 0.35 , By= 4.0 sin 85º = 3.98 , B= 4.333401763

    2. plug into the format: |(4.898979486)^2 + (4.333401763)^2| - |(4.898979486)^2 - (4.333401763)^2| = 38
     
    Last edited: Sep 1, 2015
  2. jcsd
  3. Aug 31, 2015 #2

    jedishrfu

    Staff: Mentor

    Look at the A+B and A-B terms in your expression are they vectors or scalars?
     
  4. Aug 31, 2015 #3
    they are vectors
     
  5. Aug 31, 2015 #4

    jedishrfu

    Staff: Mentor

    So what you wrote added the lengths of the components of A and B together which is not right.

    when instead you should find the length of the new vector A+B and square it for your expression.
     
    Last edited: Sep 1, 2015
  6. Sep 1, 2015 #5
    i thought it was asking to add the components of the vector A and B while also figuring out the quantity |A+B|^2 - |A-B|^2?
     
  7. Sep 1, 2015 #6

    jedishrfu

    Staff: Mentor

    The notation |A+B| means the length of the vector A+B just as |A| means the length of The vector A.
     
  8. Sep 1, 2015 #7
    So would creating a new vector like vector C = A+B?
     
  9. Sep 1, 2015 #8

    jedishrfu

    Staff: Mentor

    Yes and then find the length of C to use in your expression similarly for the |A-B| term which is the length of the vector A-B.

    Have you drawn these four vectors on paper? The A and B represent the sides of a parallelogram and the A+B is one diagonal.

    Do you know what the other vector is?
     
  10. Sep 1, 2015 #9
    isn't the other vector the opposite diagonal to A+B?
     
  11. Sep 1, 2015 #10

    jedishrfu

    Staff: Mentor

    Yes it is.

    Did you figure out the answer now?
     
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