(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
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 )