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Question

Two vectors having equal magnitudes of A make an angle θ with each other. Find the magnitude B of the resultant vector and the angle it makes with any one of the vectors?



Your Answer
A

B = A ,  

Correct Answer
B

B = 2 A cos ,  

Your Answer
C

B =  A cos ,  

Your Answer
D

B = 2 A cos ,  


Solution

The correct option is B

B = 2 A cos ,  


The magnitude of the resultant will be 

B=A2+A2+2AAcosθ 

=2A2+(1+cosθ) 

=4A2cos2θ2 

= 2 A cos θ2 

The resultant will make an angle α with the first vector where, 

tanα=A sinθA + A cosθ 

      =2 A sinθ2 cos θ22 A cos2 θ2 

( sin 2 θ = 2 sin θ cos θ , cos 2 θ = 2 cos2 θ - 1 )  

= tanθ2

Therefore , α=θ2  

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