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Question

# Two vectors of magnitude 3 units and 4 units respectively. What should be the angle between them if the magnitude of the resultant is 1 unit ?

A
180o
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B
90o
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C
60o
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D
0
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Solution

## The correct option is B 180oGiven:Magnitude of first vector, (say) P=3 units.Magnitude of second vector, (say) Q=4 units.Magnitude of resultant vector (say) R=1 unit.Now, the magnitude of resultant vector R, is given by,R=√(P2+Q2+2PQcosθ) ..................(1)where, θ is the angle between two vectors. Using the given values in equation (1), we get,1=√(32+42+2(3)(4)cosθ)∴1=√(25+24cosθ .....................(2)Squaring both the sides of equation (2), we get,1=25+24cosθ∴cosθ=−2424∴cosθ=−1∴θ=180∘

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