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The resultant of two forces each of magnitude P acting at 60° is
a) 2P
b) 3P
c) (3)
d) (2)P
Answers
Explanation:
The resultant of two forces of magnitude P acting at point is under root 2p. What is the angle between the vectors?
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4 Answers

Reon John, Maths Enthusiast.
Answered February 18, 2017
The forces are perpendicular. That is angle between them is 90 degrees.
It can be found by parallelogram law of vector addition.

In this case when you put Q=P ,R= root2 P and theta=ø
You get 2P^2 cos ø=0
Which implies cos ø=0 therefore ø=90 deg.
In simpler terms you can imagine a sqaure of side P and Resultant is given by the diagonal according to Parallelogram law. The length of diagonal will be root2 P by Pythagoras theorem.
The angles in a sqaure are right angles which again gives you
Angle between two forces is 90.
Let us suppose angle between two forces P be A radian.
P + P = √2 P.
√(|P|^2 + |P|^2 + 2 . |P|^2 Cos(A) ) = √2 |P| .
After cancelling |P| from both side we get,
=> √(2 + 2 Cos(A) ) = √2 .
=> 2 Cos(A/2) = √2 .
=> Cos(A/2) = (1/√2) .
=> A/2 = (π/4) . ( As angle between two vectors is always acute).
=> A = (π/2) .
Hope it helps you .
Have a good day !!