Pleass give solution for que 26 - Physics - Rest and Motion Kinematics

Question

Pleass give solution for que 26

Anshu Agrawal · Accepted Answer

Solution:
Given R2 = P2 + Q2 + 2PQcosθ
equation 1

now when magnitude of q is doubled it makes 900 with the
P vector
<img alt="solution" src=
"https://d1hj4to4g9ba46%20cloudfront%20net/questions/2107749_981357_ans_f492c0b4a83b46c5945456bf2b613e1c%20png">

So as we know the angle between the vectors are :

Tan θ = Bsinθ/(A+Bcosθ)  Tan 90o = 2Qsinθ/(P+2Qcosθ) 
  As Tan 90o = infinity​  so,  P+2Qcosθ=  0 or cosθ = -P/2Q
 equation 2  substituting in equation 1  we have:   R2 = P2 + Q2  + 2PQ(-P/2Q)   R2 = P2 + Q2  - P2  or,  R2 =  Q2   or , R = Q