2. Two vectors having equal magnitudes A make an angle with each other. The
magnitude and direction of the resultant are respectively:
(A) 2Acos theta/2 along bisector
(B) Acos theta/2
at 45° from one vector
(C) Acos theta/2, along bisector
(D) Asin theta /2 , along bisector
Answers
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Step-by-step explanation:
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
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