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Question

Two vectors whose magnitudes are in ratio 1:2 gives resultant of magnitude 30. If angle between these two vectors is 120, then the magnitude of two vectors will be

A
103,203
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B
53,103
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C
6,26
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D
23,43
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Solution

The correct option is A 103,203
Let the magnitude of the two vectors be x and 2x then:
Magnitude of resultant =x2+(2x)2+4x2cosθ=30
Given : θ=120o
x×5+4(12)=30(cos120o=1/2)
x=303=103
So the magnitudes of the two forces are: 103 and 203.

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