Question

Topic: Vectors Q. Two vectors of equal magnitude (F) are at an angle Θ . Find out resultant vector. Pls post a picture of written answer.

Answer 1

Answer:

We have,

Two vectors having equal magnitude makes an ∠θ

Let the magnitude of each vector be A is:

R=  

(A  

2

+A  

2

+2A×Acosθ)

​  

 

=  

[2A  

2

(1+cosθ)]

​  

 

2A  

2

×2cos  

2

θ

​  

 

​  

 

=2Acos  

2

θ

​  

 

Now,

Direction :

Let angle between any one of vectors and thne resulatant be θ

tanθ=  

Acosθ+A

Asinθ

​  

 

=  

1+cosθ

Sinθ

​  

 

=  

2cos  

2

 

2

θ

​  

 

2sin  

2

θ

​  

.cos  

2

θ

​  

 

​  

 

By using,   sinθ=2sin  

2

θ

​  

cos  

2

θ

​  

 and 1+cosθ=2cos  

2

 

2

θ

​  

 

=tan  

2

θ

​  

 

It means that, tanθ  

′

=tan  

2

θ

​  

 

θ=  

2

θ

​