when two vectors magnitude A and B are inclined at angle theta the magnitude of their resultant is 2A if the first vector is doubled the magnitude of resultant becomes 3A. find the ratio of A^2 to B^2
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Explanation:
When the angle is θ, the magnitude of resultant is
2P=
P
2
+Q
2
+2PQcosθ
(1)
When the angle is 180−θ, the magnitude of resultant is
P=
P
2
+Q
2
+2PQcos(180−θ)
(2)
Squaring and adding the two equations, we get
2P
2
+2Q
2
=5P
2
2Q
2
=3P
2
Q
P
=
3
2
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