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Maximum angle between resultant and original vector

  1. May 28, 2016 #1
    1. The problem statement, all variables and given/known data

    Two vectors of magnitude 5 units and 3 units are added such that the angle between the resultant and the vector of magnitude 5units is maximum. Find this angle.

    2. Relevant equations


    3. The attempt at a solution

    Knowing that the resultant vector makes a smaller angle with a vector of larger magnitude, I tried to draw some diagrams but they proved to be of little help.

    Further, the max. angle can't be 180 degrees or 0 degree for obvious reasons.


    I know PF does not provide complete solutions but I would be thankful for any assistance provided.
     
  2. jcsd
  3. May 28, 2016 #2
    First Try and find the angle between the vector and the resultant in terms of the angle between the two vectors.
     
    Last edited: May 28, 2016
  4. May 30, 2016 #3
    Sahil ,

    In case you have worked out the problem , do you mind checking the answer ?

    37°
     
  5. May 30, 2016 #4
    According to me the answer is
    90° + 37° = 127°
     
  6. May 30, 2016 #5
    Thanks .

    I think what you have stated is the angle between the two vectors such that the angle between the resultant and vector of magnitude 5 units is maximum . I might be wrong .

    Would you like to reconsider your answer ?
     
  7. May 30, 2016 #6
    I think my answer is correct

    cosx= -3/5 => x=90+37
     
  8. May 30, 2016 #7
    This is the angle between the two vectors , not between the resultant and vector of magnitude 5 units .
     
  9. May 30, 2016 #8
    Sorry, i didnt read the question carefully. You are correct.

    tan y = (3*4/5)/(5-3*3/5) = 3/4 => y= 37
     
  10. May 30, 2016 #9
    Alright :smile:
     
  11. May 30, 2016 #10

    haruspex

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    Draw a line OP for the vector of 5 units. From the tip of that vector, P, you can draw another line of 3 units. What is the locus of points Q where that might end? Which of these maximises the angle POQ?
     
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