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Question

Let ¯¯¯a,¯¯b, ¯¯c be non coplanar vectors. The vectors 3¯¯¯a2¯¯b4¯¯c,¯¯¯a+2¯¯c, 2¯¯¯a+¯¯b+3¯¯c are

A
Linearly dependent
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B
Linearly independent
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C
Collinear
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D
Non collinear
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Solution

The correct option is A Linearly dependent
Vectors are coplanar so we get
3a2b4c=λ(a+2c)+μ(2a+b+3c)
Solving
3=λ2μ ------(1)
μ=2 , λ=1
So there Vectors are Linerly dependent

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