Maximum angle between resultant and original vector

In summary: The locus of points Q where that might end is the vector made by the points (Q, P). That vector makes the angle POQ with the line OP.The locus of points Q where that might end is the vector made by the points (Q, P). That vector makes the angle POQ with the line OP.
  • #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.
 
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  • #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
Sahil ,

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

37°
 
  • #4
conscience said:
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
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
conscience said:
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
This is the angle between the two vectors , not between the resultant and vector of magnitude 5 units .
 
  • #8
conscience said:
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
Alright :smile:
 
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  • #10
Shivansh Mathur said:
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?
 

1. What is the maximum angle between the resultant vector and the original vector?

The maximum angle between the resultant vector and the original vector is 90 degrees.

2. How is the maximum angle between the resultant and original vector calculated?

The maximum angle between the resultant and original vector is calculated using the dot product of the two vectors. The formula is cosθ = (a · b) / (|a| * |b|), where θ is the angle between the two vectors, a and b.

3. Why is the maximum angle between the resultant and original vector important in physics?

The maximum angle between the resultant and original vector is important in physics because it helps determine the direction and magnitude of the resultant vector when two or more vectors are added together. It also plays a role in understanding the forces and motion of objects.

4. Can the maximum angle between the resultant and original vector be greater than 90 degrees?

No, the maximum angle between the resultant and original vector cannot be greater than 90 degrees. This is because the dot product of two vectors cannot be greater than the product of their magnitudes, and the cosine of an angle cannot exceed 1.

5. How does the maximum angle between the resultant and original vector change when the magnitudes of the original vectors change?

The maximum angle between the resultant and original vector can change when the magnitudes of the original vectors change. As the magnitudes increase, the maximum angle between the two vectors decreases. Conversely, as the magnitudes decrease, the maximum angle between the two vectors increases.

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