Physics, asked by Sarfrajahammad315, 11 months ago

(2) 45°
(3) 300
5. Two vectors have the same magnitude 'a' and they make an angle 'e' with each other. Then
magnitude of the resultant is​

Answers

Answered by rishu6845
22

Answer:

R = 2 a Cos α / 2

Explanation:

Given------> Two vectors have the same magnitude a and angle between two vectors is θ

To find ------> Magnitude of the resultant

Solution-------> ATQ,

P = a , Q = a , α = θ

We know that , by parallelogram law of vector addition ,

R² = P² + Q² + 2PQ Cosα

= a² + a² + 2 ( a ) ( a ) Cοsα

= a² + a² + 2a² Cosα

= 2a² + 2a² Cosα

= 2a² ( 1 + Cosα )

We know that,

Cos A = 2 Cos²A / 2 - 1 , applying it here , we get,

= 2a² { 1 + 2Cos² α / 2 - 1 )

= 2a² ( 2 Cos² α / 2 )

=> R² = 4 a² Cos² α / 2

Taking square root of both sides , we get ,

=> R = √ ( 4 a² Cos² α / 2 )

=> R = 2 a Cos α / 2

Additional information ----->

1) If angle made by resultant from P is Φ then ,

tan Φ = q Sin α / ( p + q Cosα )

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