Maximum angle between resultant and original vector

[Shivansh Mathur]

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.

 

[Sahil Kukreja]

First Try and find the angle between the vector and the resultant in terms of the angle between the two vectors.

 

[conscience]

Sahil ,

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

Spoiler

37°

 

[Sahil Kukreja]

Sahil ,

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

Spoiler

37°

According to me the answer is

Spoiler

90° + 37° = 127°

 

[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 .

Would you like to reconsider your answer ?

 

[Sahil Kukreja]

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

Spoiler

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

 

[conscience]

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

 

[Sahil Kukreja]

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.

Spoiler

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

 

[conscience]

Alright

 

[haruspex]

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?