the direction of the resultant p vector and q vector having angle tita and alpha is angle made by r vector with p vector then
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Resultant of two vector P and Q is R=P2+Q2+2PQcosθ.
Where θ is the angle between the two vectors.
As magnitude of Q is doubled the angle between the new resultant is 90o
Thus we get tan90o=P+2Qcosθ2Qsinθ
As tan90o=∞ we have P+2Qcosθ=0
P=−2Qcosθ
Now, R2=P2+Q2+2PQ2Q−P
R=Q
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