2 vectors have same magnitude.The magnitude of the resultant vector of these 2 vectors are same as either of both vectors.What is the angle between 2 vectors?

Question

2 vectors have same magnitude.The magnitude of the resultant vector of these 2 vectors are same as either of both vectors.What is the angle between 2 vectors?

Answer 1

R^2=R^2+R^2+2R.RCOSx

;cosx=-1/2
x=120degree

Answer 2

To find the angle between two vectors that have the same magnitude, and the magnitude of their resultant vector is the same as either of the two vectors, we can use the law of cosines.

Let's assume the magnitude of both vectors is 'a', and the angle between them is 'θ'.

The magnitude of the resultant vector is also 'a', according to the question.

Using the law of cosines, we have:

a^2 = a^2 + a^2 - 2(a)(a)(cos(θ))

Simplifying the equation:

a^2 = 2a^2 - 2a^2(cos(θ))

a^2 = -2a^2(cos(θ))

Dividing by -2a^2:

1 = cos(θ)

Therefore, the angle between the two vectors is θ = cos^(-1)(1) = 0 degrees.

So, the angle between the two vectors is 0 degrees, which means they are collinear or completely in the same direction.