Question

two forces each of magnitude f have a resultant of the same magnitude f the angle between two forces is
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Answer 1

Given :-

◉ Two forces each of magnitude f have a resultant of the same magnitude f

To Find :-

◉ Angle between two vectors.

Solution :-

Let the vectors be A & B of magnitude f

We know,

⇒ |A + B| = √(A² + B² + 2ABcosθ)

But the resultant is also given as f

⇒ f = √(f² + f² + 2f²cosθ)

⇒ f = √(2f² + 2f²cosθ)

⇒ f = f√{ 2(1 + cos θ) }

⇒ 1 = √( 2×2×cos² θ/2 )

[ ∵ 1 + cos θ = 2 cos² θ/2 ]

⇒ 1 = √4cos²θ/2

⇒ 1 = 2cosθ/2

⇒ 1/2 = cos θ/2

But, we know

• cos 60° = 1/2

⇒ cos 60° = cos θ/2

Comparing both sides, we have

⇒ 60° = θ/2

⇒ θ = 120°

Hence, The angle between the two vectors is 120°.

Some Information :-

◉ Resultant of two vectors A and B is given by:

• R² = A² + B² + 2ABcosθ

where, R = A + B

◉ Subtraction of two vectors A and B is given by:

• R² = A² + B² + 2ABcosθ

Where,

θ is the angle between the two vectors after shifting one of the two vectors. Because, A - B = A + (-B)