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Question

The two vectors a and b are non-collinear then at what value of x the vectors c=(2x3)a+b and d=(2x+5)ab are collinear ?

A
12
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B
12
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C
13
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D
None of these
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Solution

The correct option is D 12
Given vectors c and d are collinear
So we have c=λd , for some λ
(2x3)a+b=λ(2x+5)aλb
((2λ2)x+5λ+3)a(1+λ)b=0
Given that a and b are not collinear , so we get
((2λ2)x+5λ+3)=0 and 1+λ=0
So we get λ=1
If we substitute the value of λ in other equation , we get (4)x2=0
x=12
Therefore the correct option is A

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