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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 180o
Given:
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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