Maximum angle between resultant and original vector

1. May 28, 2016

Shivansh Mathur

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. May 28, 2016

Sahil Kukreja

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
3. May 30, 2016

conscience

Sahil ,

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

37°

4. May 30, 2016

Sahil Kukreja

According to me the answer is
90° + 37° = 127°

5. May 30, 2016

conscience

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 .

6. May 30, 2016

Sahil Kukreja

I think my answer is correct

cosx= -3/5 => x=90+37

7. May 30, 2016

conscience

This is the angle between the two vectors , not between the resultant and vector of magnitude 5 units .

8. May 30, 2016

Sahil Kukreja

Sorry, i didnt read the question carefully. You are correct.

tan y = (3*4/5)/(5-3*3/5) = 3/4 => y= 37

9. May 30, 2016

conscience

Alright

10. May 30, 2016

haruspex

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?