Maximum angle between resultant and original vector

  • #1

Homework Statement



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.

Homework Equations




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.
 

Answers and Replies

  • #2
First Try and find the angle between the vector and the resultant in terms of the angle between the two vectors.
 
Last edited:
  • #3
232
36
Sahil ,

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

37°
 
  • #4
Sahil ,

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

37°
According to me the answer is
90° + 37° = 127°
 
  • #5
232
36
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 ?
 
  • #6
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 ?
I think my answer is correct

cosx= -3/5 => x=90+37
 
  • #7
232
36
This is the angle between the two vectors , not between the resultant and vector of magnitude 5 units .
 
  • #8
This is the angle between the two vectors , not between the resultant and vector of magnitude 5 units .
Sorry, i didnt read the question carefully. You are correct.

tan y = (3*4/5)/(5-3*3/5) = 3/4 => y= 37
 
  • #9
232
36
Alright :smile:
 
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  • #10
haruspex
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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.
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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