If the resultant of two equal forces has the same magnitude, then the angle between them is

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Pradeep Kumar Verma said: (Mar 9, 2013)
Let forces are which maggnitude P. SO GIVEN IN Q. RESULTANT = P. SO WE KNOW THAT RESULTANT. R^2= A^2+B^2+2ABCOSθ THEN P^2=P^2+P^2+2P*PCOSθ P^2=P^2+P^2+2P^2COSθ 0=1+2COSθ COSθ=-1/2=COS120. SO θ=120.

Krushna said: (Jul 21, 2014)
Total space angle is 360. To forces having same magnitude. And resultant also having same of both. So 360/3 = 120.

Gunasekaran said: (Sep 4, 2014)
Why 360 is divide by 3?

Krunal said: (Sep 10, 2014)
Why 360/3?

Sathish said: (Sep 22, 2014)
Because two forces and one resultant. Resultant between two forces.

Shereif Wagdi said: (Oct 8, 2014)
According to the law of cosines, the formula is: C^2 = A^2 + B^2 - 2AB*Cos θ (notice the negative sign) The angle is equal to 60 not 120. That can be easy realized by considering the equilateral triangle, this happens only when all its angles are equal to 60 degrees.

Himanshu said: (Oct 8, 2014)
If the angle would be 120 than only at the mid xcos60+xcos60 = x.

Shashi said: (Dec 6, 2014)
Can any one can explain in detail?

Vishal said: (Jan 21, 2015)
Let F1 = 1 and F2 = 1. We know, cos60 = 1/2. When 2 forces are acting, both making 60 degrees with the horizontal, we add the angle. (60+60 = 120). i.e, cos60+cos60 = 1 (which is equal to either of the forces).

Qamar said: (Feb 1, 2015)
Let R = f then, f^2 = f^2+f^2+2f.fcosa. -f^2/2f^2 = cosa. cosa = -1/2. a = 120.

Krishna said: (Aug 9, 2015)
cos(120) = cos(90+30) = -sin30 = -0.5.

Murali Raj K said: (Sep 26, 2015)
Both the forces are equal thus the resultant is also equal. Total angle is 360. Three forces are acting equally thus 360/3=120.

Abdul Khaleque said: (Oct 19, 2015)
p2 = p2+p2+2p.pcosθ. p2 = 2p2+2p2cosθ. -p2 = 2p2cosθ. cosθ = -1/2. θ = 120.

Tushar Chakraborty said: (Nov 3, 2015)

Law of Cosine- R^2=P^2+Q^2-2PQ Cosθ So θ = 60° When Forces are Nose to tail, θ = 60°

When Forces are Tail to Tail, θ = 180°-60° = 120°

Shams said: (Nov 12, 2015)
The angle is 60 and not 120. It can be clearly understood from equilateral triangle and total angle in a triangle. And also from the cosine rule: A^2 = B^2+C^2-2BC cosA.

Musliu said: (Feb 19, 2016)
The correct answer is 120 bc the magnitude re the same. So therefore R = P the Law of cosine R^2 = R^2 +R^2 - 2R*R (Cosθ). R^2 - 2 R^2 = - 2R^2COSθ. - R^2/R^2 = - 2COSθ. 1/2 = COSθ. Cos^-10.5 = y. y = 120.

Hamed said: (Jul 28, 2016)
2 x p x cos 120 = R. p = R.

Ankit Ughade said: (Aug 9, 2016)
For getting the equilibrium condition all these forces must have the same angle to each other. Hence 360/3 = 120.

P.Chilambarasan said: (Aug 26, 2016)
R^2 = P^2 + q^2 + 2pq Cosθ. R = P = Q = F. Substitute F in the equation, you get Cosθ = -1. So, θ = 180°.

Dhanendra said: (Sep 23, 2016)
Correct answer will be 60θ as in fcosθ plus fcosθ equal to f which gives θ equal to 60θ.

Srinu said: (Sep 29, 2016)
It is based triangle law of forces.

Komal said: (Oct 14, 2016)
It is based on the law of parallelogram. Two adjacent sides having forces say 'P' & 'Q' then resultant 'R' is given by, R^2 = P^2 + Q^2 + 2PQ Cosθ. Solving this equation taking P = Q will get answer as 120.

Jitendra Mittal said: (Feb 17, 2017)
Let forces are which magnitude P. SO, GIVEN IN Q. RESULTANT = P. SO WE KNOW THAT RESULTANT. R^2 = A^2+B^2+2ABCOSθ THEN P^2 = P^2+P^2+2P^2COSθ. P^2 = P^2+P^2+2P^2COSθ. 0=1+2COSθ. COSθ=-1/2=COS120. SO, θ=120.

Punith said: (Feb 23, 2017)
Why 120° why not the answer be 90°?

Mohan said: (Mar 16, 2017)
Resultant force is equal to either of two forces. Not that all forces have a same magnitude.

Ajay said: (Sep 16, 2017)
Can anyone tell exact explanation?

Abe said: (Oct 6, 2017)
R= √(A^2+B^2+2ABcosθ). Here A=F,B=F ;We need R=F squaring on bhs. F^2 =2F^2+2F^2cosα on solving, -F^2=2F^2cosα. cosα=-0.5. α=120 DEGREE.

Naiya said: (Nov 25, 2017)
I think we can apply Lami's theorem.

Sachin said: (Jul 14, 2018)
Based on the Law of parallelogram.

Ranga... said: (Aug 4, 2018)
Two force and one resultant. Than 360/3-120.

Vaibhav said: (Jul 25, 2020)
The resultant force is the same value of one of this either forces, so we can assume R=P, P1=P, P2=P. Let using parallelogram therom, R^2 = P1^2+P2^2+2P1P2COSθ P^2 = P^2+P^2+2P^2COSθ P^2 = 2P^2+2P^2COSθ 2P^2COSθ = -P^2 And θ=120°.

S V Manikandan. said: (Nov 20, 2020)
The two forces acting with the same magnitude and resultant too same magnitude. So the angle between each two forces is equal. So we can divide the circle into three equal segments. The angle of a circle is 360°. Then 360/3 = 120°each.

Kiran Kumar said: (May 31, 2021)
According to Lamis theorem : p/sinα+q/sinβ+r/sinγ.

Panneerselvam N said: (Oct 23, 2021)
To find the resultant R= √(A2)+(B2)+2ABcosx As given in the query, the magnitude of the force is the same and let it be f whose resultant be f too. Substituting the variables in the above equation we get f= √(f2)+(f2)+2(f2)cosx Squaring on both sides we get f2=2(f2)+2(f2)cosx f2/f2 = 2 + 2 cos x 1 - 2 = 2 cosx -1/2 = cos x Therefore x=120°.